TSTP Solution File: SWV261-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV261-1 : 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 : Thu Sep 29 15:10:40 EDT 2022
% Result : Unsatisfiable 0.75s 0.85s
% Output : Proof 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 90
% Syntax : Number of formulae : 191 ( 49 unt; 14 typ; 0 def)
% Number of atoms : 746 ( 24 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 984 ( 433 ~; 473 |; 0 &)
% ( 78 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 10 >; 11 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 601 ( 547 !; 0 ?; 601 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $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(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_SetInterval_OatLeast_type,type,
c_SetInterval_OatLeast: ( $i * $i ) > $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,
^ [V_H: $i,V_G: $i] :
refl(
( c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
<=> c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_H: $i,V_G: $i] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
<=> ! [V_H: $i,V_G: $i] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_H: $i,V_G: $i] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
<=> ! [V_H: $i,V_G: $i] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_H: $i,V_G: $i] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un__subset2_0) ).
tff(5,plain,
! [V_H: $i,V_G: $i] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_H: $i,V_G: $i] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_H: $i,V_G: $i] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_H: $i,V_G: $i] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [T_1: $i] :
refl(
( class_Orderings_Oord(tc_set(T_1))
<=> class_Orderings_Oord(tc_set(T_1)) )),
inference(bind,[status(th)],]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsarity_set_1) ).
tff(14,plain,
! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [T_1: $i] : class_Orderings_Oord(tc_set(T_1)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [T_1: $i] : class_Orderings_Oord(tc_set(T_1))
| class_Orderings_Oord(tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
class_Orderings_Oord(tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [V_i: $i,T_a: $i,V_k: $i] :
refl(
( ( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
<=> ( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [V_i: $i,T_a: $i,V_k: $i] :
rewrite(
( ( ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a)
| c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a) )
<=> ( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a)
| c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a)
| c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_SetInterval_OatLeast__iff__iff2_0) ).
tff(25,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) )
<=> ( ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a)
| ~ c_lessequals(V_k,V_i,T_a) )
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[34,28,18,9]) ).
tff(36,plain,
( ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
<=> ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(38,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
^ [V_i: $i,T_a: $i,V_k: $i] :
refl(
( ( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
<=> ( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [V_i: $i,T_a: $i,V_k: $i] :
rewrite(
( ( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| c_lessequals(V_k,V_i,T_a) )
<=> ( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| c_lessequals(V_k,V_i,T_a) )
<=> ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [V_i: $i,T_a: $i,V_k: $i] :
( ~ class_Orderings_Oord(T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| c_lessequals(V_k,V_i,T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_SetInterval_OatLeast__iff__iff1_0) ).
tff(45,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg)) )
<=> ( c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [V_i: $i,T_a: $i,V_k: $i] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) )
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oord(tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[54,48,38,18]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,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(60,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)],[59]) ).
tff(61,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(62,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)],[61,60]) ).
tff(63,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)],[62,58]) ).
tff(64,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)],[63]) ).
tff(65,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)],[64,57]) ).
tff(66,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(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(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(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ~ c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) )
<=> ( c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,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_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(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(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg))) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,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_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(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(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg))) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,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_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,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(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg))) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
~ c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg))),
inference(unit_resolution,[status(thm)],[71,65,55,35]) ).
tff(73,plain,
^ [T_1: $i] :
refl(
( class_Orderings_Oorder(tc_set(T_1))
<=> class_Orderings_Oorder(tc_set(T_1)) )),
inference(bind,[status(th)],]) ).
tff(74,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)],[73]) ).
tff(75,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(76,axiom,
! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsarity_set_2) ).
tff(77,plain,
! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1)),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ~ ! [T_1: $i] : class_Orderings_Oorder(tc_set(T_1))
| class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
class_Orderings_Oorder(tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
<=> ( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(
( ( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a)) )
<=> ( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a)) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
tff(88,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) )
<=> ( c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_OatLeast(V_x,T_a),c_SetInterval_OatLeast(V_y,T_a),tc_set(T_a))
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_SetInterval_OatLeast(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_SetInterval_OatLeast(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_set(tc_Message_Omsg)))
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[97,91,81,72]) ).
tff(99,plain,
^ [V_H: $i,V_G: $i] :
refl(
( ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
<=> ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(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_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(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_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,axiom,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__mono_0) ).
tff(103,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(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_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[108,105,98]) ).
tff(110,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(111,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)],[110]) ).
tff(112,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(113,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(114,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)],[113,112]) ).
tff(115,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)],[114]) ).
tff(116,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)],[115,111]) ).
tff(117,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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[119,116,109]) ).
tff(121,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(122,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)],[121]) ).
tff(123,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(124,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/MSC001-2.ax',cls_Set_OUnCI_0) ).
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,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
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,c_union(V_A,V_B,T_a),T_a) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,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)],[126,122]) ).
tff(128,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(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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(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(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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(129,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(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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,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(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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[130,127,120]) ).
tff(132,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(133,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)],[132]) ).
tff(134,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(135,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(136,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)],[135,134]) ).
tff(137,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)],[136]) ).
tff(138,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)],[137,133]) ).
tff(139,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(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(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(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(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(140,plain,
( ( c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(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(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(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(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(141,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(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(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(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(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)],[140]) ).
tff(142,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(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(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(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(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)],[141,139]) ).
tff(143,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(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(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,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(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(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)],[143,142]) ).
tff(145,plain,
c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(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)],[144,138,109]) ).
tff(146,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(147,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)],[146]) ).
tff(148,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(149,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(150,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)],[149]) ).
tff(151,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/MSC001-2.ax',cls_Set_OinsertE_0) ).
tff(152,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)],[151,150]) ).
tff(153,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)],[152,148]) ).
tff(154,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)],[153]) ).
tff(155,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)],[154,147]) ).
tff(156,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(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(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(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(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(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(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(157,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(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(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(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(158,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(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(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(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)],[157,156]) ).
tff(159,plain,
c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X,
inference(unit_resolution,[status(thm)],[158,155,145,131]) ).
tff(160,plain,
( c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_G,tc_Message_Omsg)
<=> c_in(v_X,v_G,tc_Message_Omsg) ),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( c_in(v_X,v_G,tc_Message_Omsg)
<=> c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_G,tc_Message_Omsg) ),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( c_in(v_X,v_G,tc_Message_Omsg)
<=> c_in(v_X,v_G,tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(163,axiom,
c_in(v_X,v_G,tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(164,plain,
c_in(v_X,v_G,tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_G,tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[164,161]) ).
tff(166,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(167,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)],[166]) ).
tff(168,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(169,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/MSC001-2.ax',cls_Set_OUnCI_1) ).
tff(170,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)],[169,168]) ).
tff(171,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)],[170]) ).
tff(172,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)],[171,167]) ).
tff(173,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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_G,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_G,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(174,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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_G,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,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(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_G,tc_Message_Omsg)
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
~ c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_G,tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[175,172,120]) ).
tff(177,plain,
$false,
inference(unit_resolution,[status(thm)],[176,165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV261-1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 02:12:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.75/0.85 % SZS status Unsatisfiable
% 0.75/0.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------