%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ064-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:23:20 AM UTC 2025
% Result : Unsatisfiable 91.42s 91.62s
% Output : Proof 91.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 137
% Syntax : Number of formulae : 496 ( 355 unt; 0 typ; 0 def)
% Number of atoms : 830 ( 631 equ)
% Maximal formula atoms : 16 ( 1 avg)
% Number of connectives : 578 ( 268 ~; 252 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 555 ( 522 !; 0 ?; 555 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(c_inter_type,type,
c_inter: ( $i * $i * $i ) > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_union_type,type,
c_union: ( $i * $i * $i ) > $i ).
tff(v_u_type,type,
v_u: $i ).
tff(v_t_type,type,
v_t: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_uminus_type,type,
c_uminus: ( $i * $i ) > $i ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(c_UNIV_type,type,
c_UNIV: $i ).
tff(c_minus_type,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(c_Mutil_Otiling_type,type,
c_Mutil_Otiling: ( $i * $i ) > $i ).
tff(v_A_type,type,
v_A: $i ).
tff(1,plain,
^ [T_a: $i] :
refl(( ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset )
<=> ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_a: $i] : ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset )
<=> ! [T_a: $i] : ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_a: $i] : ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset )
<=> ! [T_a: $i] : ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T_a: $i] : ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
tff(5,plain,
! [T_a: $i] : ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i] : ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i] : ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_a: $i] : ( c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset )
| ( c_uminus(c_UNIV,tc_set(t_a)) = c_emptyset ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_uminus(c_UNIV,tc_set(t_a)) = c_emptyset,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [T_a: $i,V_y: $i] :
refl(( ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
<=> ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
tff(14,plain,
! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_UNIV,tc_set(t_a)),tc_set(t_a)) = c_UNIV ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
c_uminus(c_uminus(c_UNIV,tc_set(t_a)),tc_set(t_a)) = c_UNIV,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) )
<=> ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
tff(23,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) )
| ( c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = c_inter(v_a,v_t,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = c_inter(v_a,v_t,t_a),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
c_inter(v_a,v_t,t_a) = c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ( c_inter(v_a,v_t,t_a) = c_emptyset )
<=> ( c_inter(v_a,v_t,t_a) = c_emptyset ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
c_inter(v_a,v_t,t_a) = c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(31,plain,
c_inter(v_a,v_t,t_a) = c_emptyset,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
c_emptyset = c_inter(v_a,v_t,t_a),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
c_uminus(c_UNIV,tc_set(t_a)) = c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(transitivity,[status(thm)],[9,32,28]) ).
tff(34,plain,
c_uminus(c_uminus(c_UNIV,tc_set(t_a)),tc_set(t_a)) = c_uminus(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
c_uminus(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(c_UNIV,tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
<=> ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
tff(40,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
c_uminus(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_uminus(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
^ [T_a: $i,V_y: $i] :
refl(( ( c_union(V_y,c_emptyset,T_a) = V_y )
<=> ( c_union(V_y,c_emptyset,T_a) = V_y ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
tff(50,plain,
! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y )
| ( c_union(c_uminus(v_t,tc_set(t_a)),c_emptyset,t_a) = c_uminus(v_t,tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_emptyset,t_a) = c_uminus(v_t,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = c_emptyset,
inference(transitivity,[status(thm)],[27,31]) ).
tff(56,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_emptyset,t_a),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
<=> ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
tff(61,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_uminus(v_t,tc_set(t_a)),c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a) = c_uminus(v_t,tc_set(t_a)),
inference(transitivity,[status(thm)],[66,56,54]) ).
tff(68,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
refl(( ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
<=> ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__assoc_0) ).
tff(73,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),t_a),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
<=> ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
tff(82,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
| ( c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),v_a,t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),v_a,t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[87,16]) ).
tff(89,plain,
^ [T_a: $i,V_y: $i] :
refl(( ( c_union(c_emptyset,V_y,T_a) = V_y )
<=> ( c_union(c_emptyset,V_y,T_a) = V_y ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
tff(93,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
| ( c_union(c_emptyset,v_a,t_a) = v_a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
c_union(c_emptyset,v_a,t_a) = v_a,
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_UNIV,
inference(transitivity,[status(thm)],[45,35,18]) ).
tff(99,plain,
c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) = c_uminus(c_UNIV,tc_set(t_a)),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) = c_emptyset,
inference(transitivity,[status(thm)],[99,9]) ).
tff(101,plain,
c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),v_a,t_a) = c_union(c_emptyset,v_a,t_a),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),v_a,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),v_a,t_a),
inference(unit_resolution,[status(thm)],[102,42]) ).
tff(104,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),tc_set(t_a)) = v_a,
inference(transitivity,[status(thm)],[103,101,97]) ).
tff(105,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(v_a,tc_set(t_a)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
c_uminus(v_a,tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
c_uminus(v_a,tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),
inference(transitivity,[status(thm)],[106,88]) ).
tff(108,plain,
c_union(c_uminus(v_a,tc_set(t_a)),v_a,t_a) = c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,tc_set(t_a)),v_a,t_a),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) = v_a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
c_uminus(c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) = v_a,
inference(unit_resolution,[status(thm)],[109,16]) ).
tff(111,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
| ( c_union(c_emptyset,c_uminus(v_a,tc_set(t_a)),t_a) = c_uminus(v_a,tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
c_union(c_emptyset,c_uminus(v_a,tc_set(t_a)),t_a) = c_uminus(v_a,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[111,95]) ).
tff(113,plain,
( ( c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset )
<=> ( c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,axiom,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(115,plain,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset,
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) )
| ( c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_inter(c_union(v_a,v_t,t_a),v_u,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_inter(c_union(v_a,v_t,t_a),v_u,t_a),
inference(unit_resolution,[status(thm)],[116,25]) ).
tff(118,plain,
c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(transitivity,[status(thm)],[117,115,32,28]) ).
tff(119,plain,
c_uminus(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
c_uminus(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[120,42]) ).
tff(122,plain,
c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) = c_uminus(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y )
| ( c_union(c_uminus(v_u,tc_set(t_a)),c_emptyset,t_a) = c_uminus(v_u,tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_emptyset,t_a) = c_uminus(v_u,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[123,52]) ).
tff(125,plain,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[117]) ).
tff(126,plain,
c_emptyset = c_inter(c_union(v_a,v_t,t_a),v_u,t_a),
inference(symmetry,[status(thm)],[115]) ).
tff(127,plain,
c_emptyset = c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(transitivity,[status(thm)],[126,125]) ).
tff(128,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_emptyset,t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_emptyset,t_a),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_uminus(v_u,tc_set(t_a)),c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),
inference(unit_resolution,[status(thm)],[130,63]) ).
tff(132,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a) = c_uminus(v_u,tc_set(t_a)),
inference(transitivity,[status(thm)],[132,129,124]) ).
tff(134,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(v_a,v_t,t_a),t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(v_a,v_t,t_a),t_a) = c_uminus(v_u,tc_set(t_a)),
inference(transitivity,[status(thm)],[134,132,129,124]) ).
tff(136,plain,
c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),c_union(v_a,v_t,t_a),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(v_a,v_t,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),c_union(v_a,v_t,t_a),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(v_a,v_t,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[137,75]) ).
tff(139,plain,
c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[133]) ).
tff(140,plain,
c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
c_uminus(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[119]) ).
tff(142,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(transitivity,[status(thm)],[45,141,121,140]) ).
tff(143,plain,
c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(v_a,v_t,t_a),t_a) = c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),c_union(v_a,v_t,t_a),t_a),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a),v_t,t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(v_a,v_t,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
c_union(c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a),v_t,t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(v_a,v_t,t_a),t_a),
inference(unit_resolution,[status(thm)],[144,75]) ).
tff(146,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a),
inference(symmetry,[status(thm)],[77]) ).
tff(147,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),t_a),
inference(symmetry,[status(thm)],[68]) ).
tff(148,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a),
inference(transitivity,[status(thm)],[147,146]) ).
tff(149,plain,
c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,t_a) = c_union(c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a),v_t,t_a),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
| ( c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),v_t,t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),v_t,t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,t_a),
inference(unit_resolution,[status(thm)],[150,84]) ).
tff(152,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = v_t ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = v_t,
inference(unit_resolution,[status(thm)],[152,16]) ).
tff(154,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
| ( c_union(c_emptyset,c_uminus(v_t,tc_set(t_a)),t_a) = c_uminus(v_t,tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
c_union(c_emptyset,c_uminus(v_t,tc_set(t_a)),t_a) = c_uminus(v_t,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[154,95]) ).
tff(156,plain,
c_union(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_emptyset,c_uminus(v_t,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[55]) ).
tff(157,plain,
c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) = c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(transitivity,[status(thm)],[99,9,32,28]) ).
tff(158,plain,
c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[159,42]) ).
tff(161,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(v_t,tc_set(t_a)),
inference(transitivity,[status(thm)],[160,158,156,155]) ).
tff(162,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[163,16]) ).
tff(165,plain,
c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = v_t,
inference(transitivity,[status(thm)],[165,162,153]) ).
tff(167,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[167,16]) ).
tff(169,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
| ( c_union(c_emptyset,v_t,t_a) = v_t ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
c_union(c_emptyset,v_t,t_a) = v_t,
inference(unit_resolution,[status(thm)],[169,95]) ).
tff(171,plain,
c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),v_t,t_a) = c_union(c_emptyset,v_t,t_a),
inference(monotonicity,[status(thm)],[100]) ).
tff(172,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),v_t,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),v_t,t_a),
inference(unit_resolution,[status(thm)],[172,42]) ).
tff(174,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),tc_set(t_a)) = v_t,
inference(transitivity,[status(thm)],[173,171,170]) ).
tff(175,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(v_t,tc_set(t_a)),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
c_uminus(v_t,tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
c_uminus(v_t,tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),
inference(transitivity,[status(thm)],[176,168]) ).
tff(178,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_t,tc_set(t_a)),v_t,t_a),
inference(monotonicity,[status(thm)],[177,166]) ).
tff(179,plain,
c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[162]) ).
tff(180,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
| ( c_union(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(v_a,c_uminus(v_t,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
c_union(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(v_a,c_uminus(v_t,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[180,84]) ).
tff(182,plain,
c_union(v_a,c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
c_union(c_uminus(c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(v_a,c_uminus(v_t,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[110]) ).
tff(184,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(185,plain,
c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[184,42]) ).
tff(186,plain,
c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(v_t,tc_set(t_a)),
inference(transitivity,[status(thm)],[185,183,182,156,155]) ).
tff(187,plain,
c_uminus(c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
c_uminus(c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[188,16]) ).
tff(190,plain,
c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(transitivity,[status(thm)],[190,187,179,164]) ).
tff(192,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[193,63]) ).
tff(195,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
c_uminus(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_t,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[196,42]) ).
tff(198,plain,
c_uminus(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_UNIV,
inference(transitivity,[status(thm)],[197,195,192,178,151,149,145,143,138,136,122,119,35,18]) ).
tff(199,plain,
c_uminus(c_uminus(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_UNIV,tc_set(t_a)),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
c_uminus(c_uminus(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[200,16]) ).
tff(202,plain,
c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) = c_emptyset,
inference(transitivity,[status(thm)],[202,199,9]) ).
tff(204,plain,
c_union(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_emptyset,c_uminus(v_a,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
| ( c_union(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(v_t,c_uminus(v_a,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(206,plain,
c_union(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(v_t,c_uminus(v_a,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[205,84]) ).
tff(207,plain,
c_union(v_t,c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_minus(v_t,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
^ [T_a: $i,V_B: $i] :
refl(( ( c_union(c_UNIV,V_B,T_a) = c_UNIV )
<=> ( c_union(c_UNIV,V_B,T_a) = c_UNIV ) )),
inference(bind,[status(th)],[]) ).
tff(209,plain,
( ! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV )
<=> ! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV ) ),
inference(quant_intro,[status(thm)],[208]) ).
tff(210,plain,
( ! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV )
<=> ! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV ) ),
inference(rewrite,[status(thm)],[]) ).
tff(211,axiom,
! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
tff(212,plain,
! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV ),
inference(modus_ponens,[status(thm)],[211,210]) ).
tff(213,plain,
! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV ),
inference(skolemize,[status(sab)],[212]) ).
tff(214,plain,
! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV ),
inference(modus_ponens,[status(thm)],[213,209]) ).
tff(215,plain,
( ~ ! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV )
| ( c_union(c_UNIV,c_uminus(v_t,tc_set(t_a)),t_a) = c_UNIV ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
c_union(c_UNIV,c_uminus(v_t,tc_set(t_a)),t_a) = c_UNIV,
inference(unit_resolution,[status(thm)],[215,214]) ).
tff(217,plain,
c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_UNIV,c_uminus(v_t,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[98]) ).
tff(218,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(219,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),
inference(unit_resolution,[status(thm)],[218,75]) ).
tff(220,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a) = c_uminus(v_u,tc_set(t_a)),
inference(transitivity,[status(thm)],[219,132,129,124]) ).
tff(221,plain,
c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),v_t,t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),v_t,t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),
inference(unit_resolution,[status(thm)],[222,75]) ).
tff(224,plain,
c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),v_t,t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(transitivity,[status(thm)],[223,221,122,119,44]) ).
tff(225,plain,
c_union(c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),v_t,t_a),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),v_t,t_a),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),c_union(v_t,c_uminus(v_t,tc_set(t_a)),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
c_union(c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),v_t,t_a),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),c_union(v_t,c_uminus(v_t,tc_set(t_a)),t_a),t_a),
inference(unit_resolution,[status(thm)],[226,75]) ).
tff(228,plain,
c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),c_union(v_t,c_uminus(v_t,tc_set(t_a)),t_a),t_a) = c_union(c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),v_t,t_a),c_uminus(v_t,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
v_t = c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[153]) ).
tff(230,plain,
v_t = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),
inference(transitivity,[status(thm)],[229,179,164]) ).
tff(231,plain,
c_union(v_t,c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(v_t,c_uminus(v_t,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
| ( c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[233,84]) ).
tff(235,plain,
c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
c_union(c_UNIV,c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[217]) ).
tff(237,plain,
c_UNIV = c_union(c_UNIV,c_uminus(v_t,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[216]) ).
tff(238,plain,
( ~ ! [T_a: $i,V_B: $i] : ( c_union(c_UNIV,V_B,T_a) = c_UNIV )
| ( c_union(c_UNIV,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_UNIV ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
c_union(c_UNIV,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_UNIV,
inference(unit_resolution,[status(thm)],[238,214]) ).
tff(240,plain,
c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_UNIV,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[98]) ).
tff(241,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
| ( c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(242,plain,
c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[241,84]) ).
tff(243,plain,
c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[133]) ).
tff(244,plain,
c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(246,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[245,16]) ).
tff(247,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
| ( c_union(c_emptyset,c_uminus(v_u,tc_set(t_a)),t_a) = c_uminus(v_u,tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
c_union(c_emptyset,c_uminus(v_u,tc_set(t_a)),t_a) = c_uminus(v_u,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[247,95]) ).
tff(249,plain,
c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_emptyset,
inference(transitivity,[status(thm)],[117,115]) ).
tff(250,plain,
c_union(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(c_emptyset,c_uminus(v_u,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)) = c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(transitivity,[status(thm)],[99,9,126,125]) ).
tff(252,plain,
c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[253,42]) ).
tff(255,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(v_u,tc_set(t_a)),
inference(transitivity,[status(thm)],[254,252,250,248]) ).
tff(256,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[255]) ).
tff(257,plain,
c_uminus(c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = v_u ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(259,plain,
c_uminus(c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = v_u,
inference(unit_resolution,[status(thm)],[258,16]) ).
tff(260,plain,
v_u = c_uminus(c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
v_u = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),
inference(transitivity,[status(thm)],[260,257,246,244]) ).
tff(262,plain,
c_union(v_u,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[261]) ).
tff(263,plain,
c_union(v_u,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(v_t,c_uminus(v_t,tc_set(t_a)),t_a),
inference(transitivity,[status(thm)],[262,242,240,239,237,236,235,232]) ).
tff(264,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),v_a,t_a) = c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),
inference(monotonicity,[status(thm)],[133]) ).
tff(265,plain,
c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),v_a,t_a),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),v_a,t_a),t_a),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),v_a,t_a),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),v_a,t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),v_a,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),v_a,t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),v_a,t_a),t_a),
inference(unit_resolution,[status(thm)],[268,75]) ).
tff(270,plain,
c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(transitivity,[status(thm)],[139,122,119,44]) ).
tff(271,plain,
c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),v_a,t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a),
inference(monotonicity,[status(thm)],[270]) ).
tff(272,plain,
c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_a,t_a) = c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),v_a,t_a),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a) = c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),
inference(transitivity,[status(thm)],[147,146,272,269,267]) ).
tff(274,plain,
c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(v_u,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a) = c_union(c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),t_a),c_union(v_t,c_uminus(v_t,tc_set(t_a)),t_a),t_a),
inference(monotonicity,[status(thm)],[273,263]) ).
tff(275,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(v_u,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(276,plain,
c_union(c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(v_u,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[275,75]) ).
tff(277,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
| ( c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),v_u,t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(278,plain,
c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),v_u,t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,t_a),
inference(unit_resolution,[status(thm)],[277,84]) ).
tff(279,plain,
c_uminus(v_u,tc_set(t_a)) = c_union(c_uminus(v_u,tc_set(t_a)),c_emptyset,t_a),
inference(symmetry,[status(thm)],[124]) ).
tff(280,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
| ( c_union(c_emptyset,v_u,t_a) = v_u ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(281,plain,
c_union(c_emptyset,v_u,t_a) = v_u,
inference(unit_resolution,[status(thm)],[280,95]) ).
tff(282,plain,
c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),v_u,t_a) = c_union(c_emptyset,v_u,t_a),
inference(monotonicity,[status(thm)],[100]) ).
tff(283,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),v_u,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),tc_set(t_a)),v_u,t_a),
inference(unit_resolution,[status(thm)],[283,42]) ).
tff(285,plain,
c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),tc_set(t_a)) = v_u,
inference(transitivity,[status(thm)],[284,282,281]) ).
tff(286,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(v_u,tc_set(t_a)),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(288,plain,
c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[287,16]) ).
tff(289,plain,
c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)) = c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),
inference(transitivity,[status(thm)],[289,286,279,128,131]) ).
tff(291,plain,
c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),v_u,t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[290,261]) ).
tff(292,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a) = c_union(c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,tc_set(t_a)),v_u,t_a),
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
| ( c_union(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(294,plain,
c_union(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[293,84]) ).
tff(295,plain,
c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),tc_set(t_a)) = c_union(v_a,v_t,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(297,plain,
c_uminus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),tc_set(t_a)) = c_union(v_a,v_t,t_a),
inference(unit_resolution,[status(thm)],[296,16]) ).
tff(298,plain,
c_union(c_uminus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[297,133]) ).
tff(299,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(300,plain,
c_uminus(c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[299,42]) ).
tff(301,plain,
c_uminus(c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)) = c_uminus(v_u,tc_set(t_a)),
inference(transitivity,[status(thm)],[300,298,295,250,248]) ).
tff(302,plain,
c_uminus(c_uminus(c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[301]) ).
tff(303,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(304,plain,
c_uminus(c_uminus(c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[303,16]) ).
tff(305,plain,
c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)) = c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),
inference(transitivity,[status(thm)],[305,302,257,246,244]) ).
tff(307,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(309,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[308,63]) ).
tff(310,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,t_a),
inference(transitivity,[status(thm)],[310,307,292,278]) ).
tff(312,plain,
c_union(c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),v_u,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[311]) ).
tff(313,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(314,plain,
c_union(c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[313,75]) ).
tff(315,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a) = c_union(c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[314]) ).
tff(316,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(c_union(v_a,v_t,t_a),tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[142]) ).
tff(317,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a),
inference(unit_resolution,[status(thm)],[317,63]) ).
tff(319,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),
inference(unit_resolution,[status(thm)],[319,75]) ).
tff(321,plain,
c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a) = c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[320]) ).
tff(322,plain,
c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a) = c_uminus(v_u,tc_set(t_a)),
inference(transitivity,[status(thm)],[321,295,250,248]) ).
tff(323,plain,
c_union(c_union(v_a,v_t,t_a),c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),t_a) = c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[322]) ).
tff(324,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a) = c_union(c_union(v_a,v_t,t_a),c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(325,plain,
c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a) = c_union(c_union(v_a,v_t,t_a),c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[324,75]) ).
tff(326,plain,
c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a) = c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[220]) ).
tff(327,plain,
c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a) = c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),
inference(monotonicity,[status(thm)],[326]) ).
tff(328,plain,
c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a) = c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),
inference(transitivity,[status(thm)],[327,325,323,295,250,248,279,128,131]) ).
tff(329,plain,
c_union(c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a),v_u,t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[328,261]) ).
tff(330,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a),v_u,t_a) = c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),v_u,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(331,plain,
c_union(c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a),v_u,t_a) = c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),v_u,t_a),t_a),
inference(unit_resolution,[status(thm)],[330,75]) ).
tff(332,plain,
c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),v_u,t_a),t_a) = c_union(c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a),v_u,t_a),
inference(symmetry,[status(thm)],[331]) ).
tff(333,plain,
c_union(c_uminus(c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a) = c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),
inference(monotonicity,[status(thm)],[110]) ).
tff(334,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(335,plain,
c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),
inference(unit_resolution,[status(thm)],[334,42]) ).
tff(336,plain,
c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)),tc_set(t_a)) = c_uminus(v_u,tc_set(t_a)),
inference(transitivity,[status(thm)],[335,333,321,295,250,248]) ).
tff(337,plain,
c_uminus(c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[336]) ).
tff(338,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(339,plain,
c_uminus(c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[338,16]) ).
tff(340,plain,
c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[339]) ).
tff(341,plain,
c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),tc_set(t_a)) = c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),tc_set(t_a)),
inference(monotonicity,[status(thm)],[326]) ).
tff(342,plain,
c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),tc_set(t_a)) = v_u,
inference(transitivity,[status(thm)],[341,340,337,259]) ).
tff(343,plain,
c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),tc_set(t_a)),t_a) = c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),v_u,t_a),
inference(monotonicity,[status(thm)],[342]) ).
tff(344,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),tc_set(t_a)),t_a) = c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(345,plain,
c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),tc_set(t_a)),t_a) = c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[344,63]) ).
tff(346,plain,
c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_minus(c_uminus(v_a,tc_set(t_a)),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[345]) ).
tff(347,plain,
c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),v_u,t_a),
inference(transitivity,[status(thm)],[346,343]) ).
tff(348,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(v_a,v_t,t_a),v_a,t_a) = c_union(v_a,c_union(v_t,v_a,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(349,plain,
c_union(c_union(v_a,v_t,t_a),v_a,t_a) = c_union(v_a,c_union(v_t,v_a,t_a),t_a),
inference(unit_resolution,[status(thm)],[348,75]) ).
tff(350,plain,
c_union(v_a,c_union(v_t,v_a,t_a),t_a) = c_union(c_union(v_a,v_t,t_a),v_a,t_a),
inference(symmetry,[status(thm)],[349]) ).
tff(351,plain,
c_union(c_union(v_a,c_union(v_t,v_a,t_a),t_a),c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a),t_a) = c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),v_u,t_a),t_a),
inference(monotonicity,[status(thm)],[350,347]) ).
tff(352,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_union(v_a,c_union(v_t,v_a,t_a),t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_union(v_a,c_union(v_t,v_a,t_a),t_a),c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(353,plain,
c_union(c_union(c_union(v_a,c_union(v_t,v_a,t_a),t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_union(v_a,c_union(v_t,v_a,t_a),t_a),c_union(c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a),t_a),
inference(unit_resolution,[status(thm)],[352,75]) ).
tff(354,plain,
c_union(c_union(v_a,c_union(v_t,v_a,t_a),t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a) = c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),
inference(monotonicity,[status(thm)],[350,326]) ).
tff(355,plain,
c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a) = c_union(c_union(v_a,c_union(v_t,v_a,t_a),t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
c_union(c_union(v_a,v_t,t_a),c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),t_a) = c_union(c_union(c_union(v_a,v_t,t_a),v_a,t_a),c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),
inference(symmetry,[status(thm)],[325]) ).
tff(357,plain,
c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(c_union(v_a,v_t,t_a),c_union(v_a,c_union(v_t,c_uminus(v_u,tc_set(t_a)),t_a),t_a),t_a),
inference(symmetry,[status(thm)],[323]) ).
tff(358,plain,
c_union(c_emptyset,c_uminus(v_u,tc_set(t_a)),t_a) = c_union(c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),c_uminus(v_u,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[250]) ).
tff(359,plain,
c_uminus(v_u,tc_set(t_a)) = c_union(c_emptyset,c_uminus(v_u,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[248]) ).
tff(360,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a) = c_union(c_union(v_a,c_union(v_t,v_a,t_a),t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a),
inference(transitivity,[status(thm)],[132,129,124,359,358,294,357,356,355]) ).
tff(361,plain,
c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_union(c_union(v_a,c_union(v_t,v_a,t_a),t_a),c_union(v_t,c_union(c_union(c_uminus(v_u,tc_set(t_a)),v_a,t_a),v_t,t_a),t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[360]) ).
tff(362,plain,
c_uminus(v_u,tc_set(t_a)) = c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),
inference(transitivity,[status(thm)],[279,128,131]) ).
tff(363,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_uminus(v_a,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[362]) ).
tff(364,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(365,plain,
c_uminus(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[364,42]) ).
tff(366,plain,
c_uminus(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_UNIV,
inference(transitivity,[status(thm)],[365,363,361,353,351,332,329,318,316,315,312,276,274,228,225,217,216]) ).
tff(367,plain,
c_uminus(c_uminus(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_UNIV,tc_set(t_a)),
inference(monotonicity,[status(thm)],[366]) ).
tff(368,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(369,plain,
c_uminus(c_uminus(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[368,16]) ).
tff(370,plain,
c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) = c_emptyset,
inference(transitivity,[status(thm)],[370,367,9]) ).
tff(372,plain,
c_union(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_emptyset,c_uminus(v_a,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[371]) ).
tff(373,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) )
| ( c_union(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(v_u,c_uminus(v_a,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(374,plain,
c_union(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(v_u,c_uminus(v_a,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[373,84]) ).
tff(375,plain,
c_union(v_u,c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_minus(v_u,c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
c_union(v_u,c_uminus(v_a,tc_set(t_a)),t_a) = c_uminus(v_a,tc_set(t_a)),
inference(transitivity,[status(thm)],[375,372,112]) ).
tff(377,plain,
c_union(v_t,c_union(v_u,c_uminus(v_a,tc_set(t_a)),t_a),t_a) = c_union(v_t,c_uminus(v_a,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[376]) ).
tff(378,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(v_t,v_u,t_a),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(v_t,c_union(v_u,c_uminus(v_a,tc_set(t_a)),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(379,plain,
c_union(c_union(v_t,v_u,t_a),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(v_t,c_union(v_u,c_uminus(v_a,tc_set(t_a)),t_a),t_a),
inference(unit_resolution,[status(thm)],[378,75]) ).
tff(380,plain,
c_union(v_t,v_u,t_a) = c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),
inference(monotonicity,[status(thm)],[229]) ).
tff(381,plain,
c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a) = c_union(v_t,v_u,t_a),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
c_union(c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_union(v_t,v_u,t_a),c_uminus(v_a,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[381]) ).
tff(383,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(384,plain,
c_uminus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),
inference(unit_resolution,[status(thm)],[383,42]) ).
tff(385,plain,
c_union(c_uminus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) = c_union(c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),c_uminus(v_a,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[384]) ).
tff(386,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(387,plain,
c_uminus(c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[386,42]) ).
tff(388,plain,
c_uminus(c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(v_a,tc_set(t_a)),
inference(transitivity,[status(thm)],[387,385,382,379,377,207,204,112]) ).
tff(389,plain,
c_uminus(c_uminus(c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[388]) ).
tff(390,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(391,plain,
c_uminus(c_uminus(c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[390,16]) ).
tff(392,plain,
c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[391]) ).
tff(393,plain,
c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)) = v_a,
inference(transitivity,[status(thm)],[392,389,110]) ).
tff(394,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),v_a,t_a),
inference(monotonicity,[status(thm)],[393]) ).
tff(395,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_uminus(v_a,tc_set(t_a)),c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(396,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[395,63]) ).
tff(397,plain,
c_union(c_uminus(v_a,tc_set(t_a)),c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_minus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),c_uminus(v_a,tc_set(t_a)),tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[396]) ).
tff(398,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_a,tc_set(t_a)),c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(399,plain,
c_uminus(c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_a,tc_set(t_a)),c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),t_a),
inference(unit_resolution,[status(thm)],[398,42]) ).
tff(400,plain,
c_uminus(c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_UNIV,
inference(transitivity,[status(thm)],[399,397,394,108,86,77,68,45,35,18]) ).
tff(401,plain,
c_uminus(c_uminus(c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_UNIV,tc_set(t_a)),
inference(monotonicity,[status(thm)],[400]) ).
tff(402,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(403,plain,
c_uminus(c_uminus(c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[402,16]) ).
tff(404,plain,
c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)) = c_uminus(c_uminus(c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(406,plain,
c_uminus(c_uminus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),
inference(unit_resolution,[status(thm)],[405,16]) ).
tff(407,plain,
c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a) = c_uminus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[384]) ).
tff(408,plain,
c_uminus(c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),tc_set(t_a)) = c_uminus(c_uminus(c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[407]) ).
tff(409,plain,
c_uminus(c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),tc_set(t_a)) = c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),
inference(transitivity,[status(thm)],[408,406]) ).
tff(410,plain,
c_minus(v_a,c_uminus(c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),tc_set(t_a)),tc_set(t_a)) = c_minus(v_a,c_minus(c_uminus(v_t,tc_set(t_a)),v_u,tc_set(t_a)),tc_set(t_a)),
inference(monotonicity,[status(thm)],[409]) ).
tff(411,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) )
| ( c_minus(v_a,c_uminus(c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),tc_set(t_a)),tc_set(t_a)) = c_inter(v_a,c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(412,plain,
c_minus(v_a,c_uminus(c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),tc_set(t_a)),tc_set(t_a)) = c_inter(v_a,c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),t_a),
inference(unit_resolution,[status(thm)],[411,25]) ).
tff(413,plain,
c_inter(v_a,c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),t_a) = c_minus(v_a,c_uminus(c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[412]) ).
tff(414,plain,
c_inter(v_a,c_union(v_t,v_u,t_a),t_a) = c_inter(v_a,c_union(c_uminus(c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),v_u,t_a),t_a),
inference(monotonicity,[status(thm)],[380]) ).
tff(415,plain,
c_inter(v_a,c_union(v_t,v_u,t_a),t_a) = c_emptyset,
inference(transitivity,[status(thm)],[414,413,410,404,401,9]) ).
tff(416,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(v_a,v_t,t_a),v_u,t_a) = c_union(v_a,c_union(v_t,v_u,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(417,plain,
c_union(c_union(v_a,v_t,t_a),v_u,t_a) = c_union(v_a,c_union(v_t,v_u,t_a),t_a),
inference(unit_resolution,[status(thm)],[416,75]) ).
tff(418,plain,
c_union(v_a,c_union(v_t,v_u,t_a),t_a) = c_union(c_union(v_a,v_t,t_a),v_u,t_a),
inference(symmetry,[status(thm)],[417]) ).
tff(419,plain,
( c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(monotonicity,[status(thm)],[418]) ).
tff(420,plain,
( c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(symmetry,[status(thm)],[419]) ).
tff(421,plain,
( ~ c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> ~ c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(monotonicity,[status(thm)],[420]) ).
tff(422,plain,
( ~ c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> ~ c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(423,axiom,
~ c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(424,plain,
~ c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[423,422]) ).
tff(425,plain,
~ c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[424,421]) ).
tff(426,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(427,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a),
inference(unit_resolution,[status(thm)],[426,63]) ).
tff(428,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
c_UNIV = c_uminus(c_uminus(c_UNIV,tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[18]) ).
tff(430,plain,
c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),
inference(transitivity,[status(thm)],[240,239,429,34,44]) ).
tff(431,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a),
inference(monotonicity,[status(thm)],[430]) ).
tff(432,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(433,plain,
c_union(c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[432,75]) ).
tff(434,plain,
c_union(c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),v_t,t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_minus(c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[67,230]) ).
tff(435,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),v_t,t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(436,plain,
c_union(c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),v_t,t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),
inference(unit_resolution,[status(thm)],[435,75]) ).
tff(437,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a) = c_union(c_union(c_uminus(v_t,tc_set(t_a)),v_a,t_a),v_t,t_a),
inference(symmetry,[status(thm)],[436]) ).
tff(438,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a),
inference(transitivity,[status(thm)],[437,434,427]) ).
tff(439,plain,
c_union(c_union(c_uminus(v_t,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_a,tc_set(t_a)),c_uminus(v_t,tc_set(t_a)),t_a),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[438]) ).
tff(440,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] : ( c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_union(c_uminus(v_t,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_union(v_a,v_t,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(441,plain,
c_union(c_union(c_uminus(v_t,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_union(v_a,v_t,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[440,75]) ).
tff(442,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_union(v_a,v_t,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a) = c_union(c_union(c_uminus(v_t,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[441]) ).
tff(443,plain,
c_union(c_union(v_a,v_t,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a),
inference(monotonicity,[status(thm)],[133]) ).
tff(444,plain,
c_union(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),t_a) = c_union(c_union(v_a,v_t,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(symmetry,[status(thm)],[443]) ).
tff(445,plain,
c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a) = c_union(c_union(v_a,v_t,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(transitivity,[status(thm)],[132,129,124,359,358,294,444]) ).
tff(446,plain,
c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_union(v_a,v_t,t_a),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),t_a),
inference(monotonicity,[status(thm)],[445]) ).
tff(447,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) )
| ( c_uminus(c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(448,plain,
c_uminus(c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)) = c_union(c_uminus(v_t,tc_set(t_a)),c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[447,42]) ).
tff(449,plain,
c_uminus(c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)) = c_UNIV,
inference(transitivity,[status(thm)],[448,446,442,439,433,431,428,178,151,149,145,143,138,136,122,119,35,18]) ).
tff(450,plain,
c_uminus(c_uminus(c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_uminus(c_UNIV,tc_set(t_a)),
inference(monotonicity,[status(thm)],[449]) ).
tff(451,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y )
| ( c_uminus(c_uminus(c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(452,plain,
c_uminus(c_uminus(c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[451,16]) ).
tff(453,plain,
c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)) = c_uminus(c_uminus(c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[452]) ).
tff(454,plain,
c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_minus(v_t,c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_a,v_t,t_a),t_a),tc_set(t_a)),
inference(monotonicity,[status(thm)],[362]) ).
tff(455,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) )
| ( c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_inter(v_t,v_u,t_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(456,plain,
c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_inter(v_t,v_u,t_a),
inference(unit_resolution,[status(thm)],[455,25]) ).
tff(457,plain,
c_inter(v_t,v_u,t_a) = c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)),
inference(symmetry,[status(thm)],[456]) ).
tff(458,plain,
c_inter(v_t,v_u,t_a) = c_emptyset,
inference(transitivity,[status(thm)],[457,454,453,450,9]) ).
tff(459,plain,
( c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(460,axiom,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(461,plain,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[460,459]) ).
tff(462,plain,
( ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) )
<=> ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(463,plain,
( ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) )
<=> ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(464,plain,
( ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset ) )
<=> ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(465,plain,
( ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) )
<=> ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ) ),
inference(monotonicity,[status(thm)],[464]) ).
tff(466,plain,
( ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) )
<=> ( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ) ),
inference(transitivity,[status(thm)],[465,463]) ).
tff(467,axiom,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(468,plain,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[467,466]) ).
tff(469,plain,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[468,462]) ).
tff(470,plain,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[469,462]) ).
tff(471,plain,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[470,462]) ).
tff(472,plain,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset )
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[471,462]) ).
tff(473,plain,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_t,v_u,t_a) != c_emptyset ) ),
inference(unit_resolution,[status(thm)],[472,461]) ).
tff(474,plain,
c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(unit_resolution,[status(thm)],[473,458]) ).
tff(475,plain,
^ [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
refl(( ( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
<=> ( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(476,plain,
( ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[475]) ).
tff(477,plain,
( ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(478,plain,
^ [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ c_in(V_a,V_A,tc_set(T_a))
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a)) )
<=> ( ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ) )),
( ( ~ c_in(V_a,V_A,tc_set(T_a))
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset ) )
<=> ( ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset ) ) )),
rewrite(( ( ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset ) )
<=> ( ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ) )),
( ( ~ c_in(V_a,V_A,tc_set(T_a))
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset ) )
<=> ( ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ) )),
( ( ~ c_in(V_a,V_A,tc_set(T_a))
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a)) )
<=> ( ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a))
| c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a)) ) )),
rewrite(( ( ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a))
| c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a)) )
<=> ( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ) )),
( ( ~ c_in(V_a,V_A,tc_set(T_a))
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a)) )
<=> ( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(479,plain,
( ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( ~ c_in(V_a,V_A,tc_set(T_a))
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[478]) ).
tff(480,axiom,
! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( ~ c_in(V_a,V_A,tc_set(T_a))
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling_OUn_0) ).
tff(481,plain,
! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[480,479]) ).
tff(482,plain,
! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[481,477]) ).
tff(483,plain,
! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[482]) ).
tff(484,plain,
! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[483,476]) ).
tff(485,plain,
( c_in(v_a,v_A,tc_set(t_a))
<=> c_in(v_a,v_A,tc_set(t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(486,axiom,
c_in(v_a,v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(487,plain,
c_in(v_a,v_A,tc_set(t_a)),
inference(modus_ponens,[status(thm)],[486,485]) ).
tff(488,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
| ~ c_in(v_a,v_A,tc_set(t_a))
| c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
| ~ c_in(v_a,v_A,tc_set(t_a))
| c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(489,plain,
( ( c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ~ c_in(v_a,v_A,tc_set(t_a)) )
<=> ( ~ c_in(v_a,v_A,tc_set(t_a))
| c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(490,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
| c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ~ c_in(v_a,v_A,tc_set(t_a)) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
| ~ c_in(v_a,v_A,tc_set(t_a))
| c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ) ),
inference(monotonicity,[status(thm)],[489]) ).
tff(491,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
| c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ~ c_in(v_a,v_A,tc_set(t_a)) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
| ~ c_in(v_a,v_A,tc_set(t_a))
| c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ) ),
inference(transitivity,[status(thm)],[490,488]) ).
tff(492,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
| c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ~ c_in(v_a,v_A,tc_set(t_a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(493,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i,V_t: $i] :
( c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ( c_inter(V_a,V_t,T_a) != c_emptyset )
| ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
| ~ c_in(V_a,V_A,tc_set(T_a)) )
| ~ c_in(v_a,v_A,tc_set(t_a))
| c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(modus_ponens,[status(thm)],[492,491]) ).
tff(494,plain,
( c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| ( c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset )
| ~ c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(unit_resolution,[status(thm)],[493,487,484]) ).
tff(495,plain,
c_inter(v_a,c_union(v_t,v_u,t_a),t_a) != c_emptyset,
inference(unit_resolution,[status(thm)],[494,474,425]) ).
tff(496,plain,
$false,
inference(unit_resolution,[status(thm)],[495,415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ064-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 02:45:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 91.42/91.62 % SZS status Unsatisfiable
% 91.42/91.62 % SZS output start Proof
% See solution above
% 91.54/91.69 % E exiting
%------------------------------------------------------------------------------