%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV251-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:31:51 AM UTC 2025
% Result : Unsatisfiable 2.20s 2.40s
% Output : Proof 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 46
% Syntax : Number of formulae : 105 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 432 ( 34 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 538 ( 220 ~; 272 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 388 ( 356 !; 0 ?; 388 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(v_G_type,type,
v_G: $i ).
tff(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
tff(c_union_type,type,
c_union: ( $i * $i * $i ) > $i ).
tff(v_H_type,type,
v_H: $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(1,plain,
( ~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
<=> ~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
<=> c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(6,plain,
c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ 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))
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,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_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) ) )),
inference(bind,[status(th)],[]) ).
tff(11,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_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) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,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(13,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) )
<=> ( c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ 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_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
^ [V_H: $i,V_G: $i] :
refl(( ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
<=> ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).
tff(28,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[33,30,23]) ).
tff(35,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(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)) )
<=> ! [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)],[35]) ).
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)) )
<=> ! [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(38,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(39,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)],[38,37]) ).
tff(40,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)],[39]) ).
tff(41,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)],[40,36]) ).
tff(42,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_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [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_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,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_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,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_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[44,41,34]) ).
tff(46,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,c_union(V_A,V_B,T_a),T_a) )
<=> ( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
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,c_union(V_A,V_B,T_a),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,c_union(V_A,V_B,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[46]) ).
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,c_union(V_A,V_B,T_a),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,c_union(V_A,V_B,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_OUn__iff_2) ).
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,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
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,c_union(V_A,V_B,T_a),T_a) ),
inference(skolemize,[status(sab)],[50]) ).
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,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,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,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,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,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,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,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[55,52,45]) ).
tff(57,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(58,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [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)],[57]) ).
tff(59,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ! [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(60,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(61,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)],[60,59]) ).
tff(62,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)],[61]) ).
tff(63,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) )
<=> ( ~ ! [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_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ( c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) )
<=> ( c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [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_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [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_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) )
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[69,63,34]) ).
tff(71,plain,
^ [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
refl(( ( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
<=> ( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
^ [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
rewrite(( ( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| ( V_a = V_b ) )
<=> ( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| ( V_a = V_b ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_Oinsert__iff_0) ).
tff(77,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) )
<=> ( c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X ) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X ) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,V_A,T_a)
| ( V_a = V_b )
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) )
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)
| ( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X,
inference(unit_resolution,[status(thm)],[86,80,70,56]) ).
tff(88,plain,
( c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
<=> c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
<=> c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg) ),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
<=> c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(92,plain,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[92,89]) ).
tff(94,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_OUn__iff_1) ).
tff(98,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[103,100,45]) ).
tff(105,plain,
$false,
inference(unit_resolution,[status(thm)],[104,93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV251-1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.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
% 0.13/0.35 % DateTime : Fri Jun 20 09:33:17 EDT 2025
% 0.13/0.35 % CPUTime :
% 2.20/2.40 % SZS status Unsatisfiable
% 2.20/2.40 % SZS output start Proof
% See solution above
% 2.30/2.50 % E exiting
%------------------------------------------------------------------------------