%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW431-1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:36:59 AM UTC 2025
% Result : Unsatisfiable 36.24s 36.42s
% Output : Proof 36.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 207
% Syntax : Number of formulae : 1148 ( 904 unt; 0 typ; 0 def)
% Number of atoms : 1652 (1415 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 858 ( 359 ~; 446 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 850 ( 829 !; 0 ?; 850 :)
% Comments :
%------------------------------------------------------------------------------
tff(heap_type,type,
heap: $i > $o ).
tff(sep_type,type,
sep: ( $i * $i ) > $i ).
tff(emp_type,type,
emp: $i ).
tff(lseg_type,type,
lseg: ( $i * $i ) > $i ).
tff(x7_type,type,
x7: $i ).
tff(x11_type,type,
x11: $i ).
tff(x1_type,type,
x1: $i ).
tff(x2_type,type,
x2: $i ).
tff(x9_type,type,
x9: $i ).
tff(x8_type,type,
x8: $i ).
tff(x13_type,type,
x13: $i ).
tff(x4_type,type,
x4: $i ).
tff(x3_type,type,
x3: $i ).
tff(x5_type,type,
x5: $i ).
tff(x10_type,type,
x10: $i ).
tff(x12_type,type,
x12: $i ).
tff(1,plain,
^ [Sigma: $i,S: $i,T: $i] :
refl(( ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',associative_commutative) ).
tff(5,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x7),sep(lseg(x11,x1),emp)) = sep(lseg(x11,x1),sep(lseg(x11,x7),emp)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
sep(lseg(x11,x7),sep(lseg(x11,x1),emp)) = sep(lseg(x11,x1),sep(lseg(x11,x7),emp)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
sep(lseg(x11,x1),sep(lseg(x11,x7),emp)) = sep(lseg(x11,x7),sep(lseg(x11,x1),emp)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
sep(lseg(x11,x12),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))) = sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(14,plain,
sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(unit_resolution,[status(thm)],[13,7]) ).
tff(15,plain,
sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(transitivity,[status(thm)],[15,12]) ).
tff(17,plain,
sep(lseg(x12,x7),sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x7),sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
sep(lseg(x12,x7),sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[18,7]) ).
tff(20,plain,
sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(transitivity,[status(thm)],[20,17]) ).
tff(22,plain,
sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[25,22]) ).
tff(27,plain,
sep(lseg(x4,x9),sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
sep(lseg(x4,x9),sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[28,7]) ).
tff(30,plain,
sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[30,27]) ).
tff(32,plain,
sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[35,32]) ).
tff(37,plain,
sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[40,37]) ).
tff(42,plain,
sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[43,7]) ).
tff(45,plain,
sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[46,7]) ).
tff(48,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[48,7]) ).
tff(50,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))) = sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))) = sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))),
inference(unit_resolution,[status(thm)],[50,7]) ).
tff(52,plain,
sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))) = sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))) = sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[57,7]) ).
tff(59,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[59,56]) ).
tff(61,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[63,7]) ).
tff(65,plain,
sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[60]) ).
tff(67,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(unit_resolution,[status(thm)],[68,7]) ).
tff(70,plain,
sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[75,7]) ).
tff(77,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[70]) ).
tff(78,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[79,76,74,67]) ).
tff(81,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[81,65,62]) ).
tff(83,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[84,49]) ).
tff(86,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(monotonicity,[status(thm)],[52]) ).
tff(88,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(unit_resolution,[status(thm)],[89,7]) ).
tff(91,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))),
inference(transitivity,[status(thm)],[91,88]) ).
tff(93,plain,
sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[93,59,56]) ).
tff(95,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[96,7]) ).
tff(98,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[98,95]) ).
tff(100,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[101,7]) ).
tff(103,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[104,7]) ).
tff(106,plain,
sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(monotonicity,[status(thm)],[52]) ).
tff(107,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[108,7]) ).
tff(110,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[92]) ).
tff(112,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[111,110,107]) ).
tff(113,plain,
sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[114,105]) ).
tff(116,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(unit_resolution,[status(thm)],[117,7]) ).
tff(119,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[122,7]) ).
tff(124,plain,
sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[124,121]) ).
tff(126,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[126,116,103,100]) ).
tff(128,plain,
sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[129,7]) ).
tff(131,plain,
sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[125]) ).
tff(133,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[119]) ).
tff(136,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[136,7]) ).
tff(138,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[138,135]) ).
tff(140,plain,
sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[144,7]) ).
tff(146,plain,
sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[146,143]) ).
tff(148,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[148,134,131,128]) ).
tff(150,plain,
sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[151,7]) ).
tff(153,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[147]) ).
tff(155,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[133]) ).
tff(157,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[158,7]) ).
tff(160,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[125]) ).
tff(161,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[162,159,157,155]) ).
tff(164,plain,
sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[162]) ).
tff(166,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[159]) ).
tff(167,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[166,165]) ).
tff(168,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[168,164,153,150,86,47]) ).
tff(170,plain,
sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[170,45,42]) ).
tff(172,plain,
sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[174,7]) ).
tff(176,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))) = sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))) = sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))),
inference(unit_resolution,[status(thm)],[176,7]) ).
tff(178,plain,
sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))) = sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))) = sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))),
inference(unit_resolution,[status(thm)],[180,7]) ).
tff(182,plain,
sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(transitivity,[status(thm)],[182,179]) ).
tff(184,plain,
sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[188,7]) ).
tff(190,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[190,187]) ).
tff(192,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[194,7]) ).
tff(196,plain,
sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[191]) ).
tff(198,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[178]) ).
tff(200,plain,
sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))),
inference(unit_resolution,[status(thm)],[201,7]) ).
tff(203,plain,
sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(transitivity,[status(thm)],[203,200]) ).
tff(205,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[209,7]) ).
tff(211,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[204]) ).
tff(212,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[213,210,208,198]) ).
tff(215,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[215,196,193]) ).
tff(217,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[218,175]) ).
tff(220,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[222,7]) ).
tff(224,plain,
sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[225,7]) ).
tff(227,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[226]) ).
tff(228,plain,
sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[228]) ).
tff(230,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[229,224,221]) ).
tff(231,plain,
sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(unit_resolution,[status(thm)],[233,7]) ).
tff(235,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[235,7]) ).
tff(237,plain,
sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[239,7]) ).
tff(241,plain,
sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[219]) ).
tff(242,plain,
sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[241,240,238]) ).
tff(243,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(246,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[245,7]) ).
tff(247,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))),
inference(unit_resolution,[status(thm)],[247,7]) ).
tff(249,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(252,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[251,7]) ).
tff(253,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[253,250]) ).
tff(255,plain,
sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(258,plain,
sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[257,7]) ).
tff(259,plain,
sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[254]) ).
tff(261,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[261]) ).
tff(263,plain,
sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[262,259,256]) ).
tff(264,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[265,246]) ).
tff(267,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(270,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[269,7]) ).
tff(271,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[185]) ).
tff(273,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(275,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[274,7]) ).
tff(276,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[276,273]) ).
tff(278,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(281,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[280,7]) ).
tff(282,plain,
sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[277]) ).
tff(283,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[182]) ).
tff(286,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[286]) ).
tff(288,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[287,276,273]) ).
tff(289,plain,
sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(291,plain,
sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[290,7]) ).
tff(292,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[286]) ).
tff(293,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[294,7]) ).
tff(296,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[296,293]) ).
tff(298,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[298,291,289]) ).
tff(300,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[301,7]) ).
tff(303,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[302]) ).
tff(304,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[297]) ).
tff(305,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(307,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[306,7]) ).
tff(308,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[307]) ).
tff(309,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[308,305]) ).
tff(310,plain,
sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[309]) ).
tff(311,plain,
sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[310,303,300,284,281,279]) ).
tff(312,plain,
sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[311]) ).
tff(313,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(314,plain,
sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[313,7]) ).
tff(315,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[314]) ).
tff(316,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[315,312]) ).
tff(317,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[316]) ).
tff(318,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[317]) ).
tff(319,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[318,271,268]) ).
tff(320,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[319]) ).
tff(321,plain,
sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(symmetry,[status(thm)],[320]) ).
tff(322,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(323,plain,
sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(unit_resolution,[status(thm)],[322,7]) ).
tff(324,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[297]) ).
tff(325,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[324]) ).
tff(326,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[325]) ).
tff(327,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(329,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[328,7]) ).
tff(330,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[329]) ).
tff(331,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[309]) ).
tff(332,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[331,330,327]) ).
tff(333,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[332]) ).
tff(334,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(335,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[334,7]) ).
tff(336,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[336,333]) ).
tff(338,plain,
sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(340,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[339,7]) ).
tff(341,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[266]) ).
tff(342,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[341,340,338]) ).
tff(343,plain,
sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[342]) ).
tff(344,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(346,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(unit_resolution,[status(thm)],[345,7]) ).
tff(347,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[316]) ).
tff(349,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(350,plain,
sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[349,7]) ).
tff(351,plain,
sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[333]) ).
tff(353,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[352,335]) ).
tff(354,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[353]) ).
tff(355,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[354,351,348]) ).
tff(356,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[355]) ).
tff(357,plain,
sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[31]) ).
tff(359,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(360,plain,
sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[359,7]) ).
tff(361,plain,
sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[361,358]) ).
tff(363,plain,
sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[362]) ).
tff(364,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(365,plain,
sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[364,7]) ).
tff(366,plain,
sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[365]) ).
tff(367,plain,
sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[366,363]) ).
tff(368,plain,
sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[367]) ).
tff(369,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(370,plain,
sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[369,7]) ).
tff(371,plain,
sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[370]) ).
tff(372,plain,
sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[371,368]) ).
tff(373,plain,
sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(375,plain,
sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[374,7]) ).
tff(376,plain,
sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[375]) ).
tff(377,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(378,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[377]) ).
tff(379,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(380,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[379,7]) ).
tff(381,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[381,378]) ).
tff(383,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[382]) ).
tff(384,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[383]) ).
tff(385,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(386,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[385,7]) ).
tff(387,plain,
sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[382]) ).
tff(388,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[388]) ).
tff(390,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[77]) ).
tff(391,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(392,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[391,7]) ).
tff(393,plain,
sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[70]) ).
tff(394,plain,
sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[394]) ).
tff(396,plain,
sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(397,plain,
sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[396]) ).
tff(398,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(399,plain,
sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[398,7]) ).
tff(400,plain,
sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[399]) ).
tff(401,plain,
sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[400,397]) ).
tff(402,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[401]) ).
tff(403,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(404,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[403,7]) ).
tff(405,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[404]) ).
tff(406,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[405,402,395,392,390]) ).
tff(407,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[406]) ).
tff(408,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(409,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[408,7]) ).
tff(410,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[106]) ).
tff(412,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[411]) ).
tff(413,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[412]) ).
tff(414,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(415,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[414,7]) ).
tff(416,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[415]) ).
tff(417,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[416,413]) ).
tff(418,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[417]) ).
tff(419,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[418]) ).
tff(420,plain,
sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[118]) ).
tff(421,plain,
sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[420]) ).
tff(422,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[422]) ).
tff(424,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[423]) ).
tff(425,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(426,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[425,7]) ).
tff(427,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[135]) ).
tff(429,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[428]) ).
tff(430,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[429,427,424,419]) ).
tff(431,plain,
sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[430]) ).
tff(432,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))) = sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(433,plain,
sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))) = sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))),
inference(unit_resolution,[status(thm)],[432,7]) ).
tff(434,plain,
sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))) = sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))),
inference(monotonicity,[status(thm)],[9]) ).
tff(435,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))) = sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(436,plain,
sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))) = sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))),
inference(unit_resolution,[status(thm)],[435,7]) ).
tff(437,plain,
sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))) = sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))),
inference(symmetry,[status(thm)],[436]) ).
tff(438,plain,
sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))) = sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))),
inference(transitivity,[status(thm)],[437,434]) ).
tff(439,plain,
sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(monotonicity,[status(thm)],[438]) ).
tff(440,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))) = sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(441,plain,
sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))) = sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))),
inference(unit_resolution,[status(thm)],[440,7]) ).
tff(442,plain,
sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))) = sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))),
inference(symmetry,[status(thm)],[441]) ).
tff(443,plain,
sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(transitivity,[status(thm)],[442,439]) ).
tff(444,plain,
sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[443]) ).
tff(445,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[444]) ).
tff(446,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))),
inference(transitivity,[status(thm)],[445,433]) ).
tff(447,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[446]) ).
tff(448,plain,
sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[447]) ).
tff(449,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(450,plain,
sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[449,7]) ).
tff(451,plain,
sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[450]) ).
tff(452,plain,
sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[451,448]) ).
tff(453,plain,
sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[452]) ).
tff(454,plain,
sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[453,431,410,407,389,386,384]) ).
tff(455,plain,
sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[454]) ).
tff(456,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(457,plain,
sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[456,7]) ).
tff(458,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[457]) ).
tff(459,plain,
sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[452]) ).
tff(460,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[459]) ).
tff(461,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[460]) ).
tff(462,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[461,458,455]) ).
tff(463,plain,
sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[462]) ).
tff(464,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(465,plain,
sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[464,7]) ).
tff(466,plain,
sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[460]) ).
tff(468,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[467]) ).
tff(469,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(470,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[469,7]) ).
tff(471,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[417]) ).
tff(472,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[471]) ).
tff(473,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[472]) ).
tff(474,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(476,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[475,7]) ).
tff(477,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[476]) ).
tff(478,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[430]) ).
tff(479,plain,
sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[452]) ).
tff(480,plain,
sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[479,478,477,474]) ).
tff(481,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[480]) ).
tff(482,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[481]) ).
tff(483,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[482,470,468]) ).
tff(484,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[483]) ).
tff(485,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[484,466,463]) ).
tff(486,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[485]) ).
tff(487,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(488,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[487,7]) ).
tff(489,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(490,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(unit_resolution,[status(thm)],[489,7]) ).
tff(491,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(493,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[492,7]) ).
tff(494,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[493]) ).
tff(495,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(496,plain,
sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[495,7]) ).
tff(497,plain,
sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[496]) ).
tff(498,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[497]) ).
tff(499,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[498]) ).
tff(500,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(501,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[500,7]) ).
tff(502,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[502,499]) ).
tff(504,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[503]) ).
tff(505,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(506,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[505,7]) ).
tff(507,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[506]) ).
tff(508,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(509,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[508,7]) ).
tff(510,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[496]) ).
tff(511,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[510]) ).
tff(512,plain,
sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[510]) ).
tff(513,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(514,plain,
sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[513,7]) ).
tff(515,plain,
sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[514]) ).
tff(516,plain,
sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[515,512]) ).
tff(517,plain,
sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[516]) ).
tff(518,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(519,plain,
sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[518,7]) ).
tff(520,plain,
sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[519]) ).
tff(521,plain,
sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[520,517,511,509]) ).
tff(522,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x12,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[521]) ).
tff(523,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(524,plain,
sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[523,7]) ).
tff(525,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x4,x9),sep(lseg(x12,x7),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[524]) ).
tff(526,plain,
sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[525,522,507,504,494]) ).
tff(527,plain,
sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[526]) ).
tff(528,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(529,plain,
sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(unit_resolution,[status(thm)],[528,7]) ).
tff(530,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x5,x3),sep(lseg(x12,x7),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(transitivity,[status(thm)],[530,527]) ).
tff(532,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(monotonicity,[status(thm)],[531]) ).
tff(533,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(534,plain,
sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(unit_resolution,[status(thm)],[533,7]) ).
tff(535,plain,
sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x10,x8),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(symmetry,[status(thm)],[534]) ).
tff(536,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(537,plain,
sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(unit_resolution,[status(thm)],[536,7]) ).
tff(538,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[537]) ).
tff(539,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[538]) ).
tff(540,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[539]) ).
tff(541,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(542,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[541,7]) ).
tff(543,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[542]) ).
tff(544,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[543,540]) ).
tff(545,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[544]) ).
tff(546,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[545]) ).
tff(547,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[546]) ).
tff(548,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[547]) ).
tff(549,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(550,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[549,7]) ).
tff(551,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[550]) ).
tff(552,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[544]) ).
tff(553,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[552]) ).
tff(554,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[553]) ).
tff(555,plain,
sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[538]) ).
tff(556,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(557,plain,
sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[556,7]) ).
tff(558,plain,
sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[557]) ).
tff(559,plain,
sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[558,555]) ).
tff(560,plain,
sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[559]) ).
tff(561,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[560]) ).
tff(562,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[561]) ).
tff(563,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[562]) ).
tff(564,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(565,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[564,7]) ).
tff(566,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[565]) ).
tff(567,plain,
sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[559]) ).
tff(568,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[567]) ).
tff(569,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[568]) ).
tff(570,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(571,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[570,7]) ).
tff(572,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))) = sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(573,plain,
sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))) = sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(unit_resolution,[status(thm)],[572,7]) ).
tff(574,plain,
sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))) = sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(symmetry,[status(thm)],[573]) ).
tff(575,plain,
sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[574]) ).
tff(576,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[575]) ).
tff(577,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[576]) ).
tff(578,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[577,571]) ).
tff(579,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[578]) ).
tff(580,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[579]) ).
tff(581,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(582,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[581,7]) ).
tff(583,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[582]) ).
tff(584,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[583,580]) ).
tff(585,plain,
sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[584]) ).
tff(586,plain,
sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[585,569,566,563]) ).
tff(587,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[586]) ).
tff(588,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(589,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[588,7]) ).
tff(590,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[589]) ).
tff(591,plain,
sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[584]) ).
tff(592,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[591]) ).
tff(593,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[592]) ).
tff(594,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[555]) ).
tff(595,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(596,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[595,7]) ).
tff(597,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[596]) ).
tff(598,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(599,plain,
sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(unit_resolution,[status(thm)],[598,7]) ).
tff(600,plain,
sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[575]) ).
tff(601,plain,
sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[537]) ).
tff(602,plain,
sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(transitivity,[status(thm)],[601,600,599]) ).
tff(603,plain,
sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[602]) ).
tff(604,plain,
sep(lseg(x4,x9),sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[603]) ).
tff(605,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(606,plain,
sep(lseg(x4,x9),sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[605,7]) ).
tff(607,plain,
sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x11,x12),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[606]) ).
tff(608,plain,
sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[607,604]) ).
tff(609,plain,
sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[608]) ).
tff(610,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(611,plain,
sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[610,7]) ).
tff(612,plain,
sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x11,x12),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[611]) ).
tff(613,plain,
sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[612,609,597,594]) ).
tff(614,plain,
sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[613]) ).
tff(615,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(616,plain,
sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[615,7]) ).
tff(617,plain,
sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x11,x12),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[616]) ).
tff(618,plain,
sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[617,614]) ).
tff(619,plain,
sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[618]) ).
tff(620,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(621,plain,
sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[620,7]) ).
tff(622,plain,
sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[621]) ).
tff(623,plain,
sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[622,619,593,590,587,554,551,548]) ).
tff(624,plain,
sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[623]) ).
tff(625,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(626,plain,
sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[625,7]) ).
tff(627,plain,
sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x5,x3),sep(lseg(x11,x12),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[626]) ).
tff(628,plain,
sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[627,624]) ).
tff(629,plain,
sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[628]) ).
tff(630,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(631,plain,
sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(unit_resolution,[status(thm)],[630,7]) ).
tff(632,plain,
sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x11,x12),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(symmetry,[status(thm)],[631]) ).
tff(633,plain,
sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(transitivity,[status(thm)],[632,629]) ).
tff(634,plain,
sep(lseg(x12,x7),sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(monotonicity,[status(thm)],[633]) ).
tff(635,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x7),sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(636,plain,
sep(lseg(x12,x7),sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(unit_resolution,[status(thm)],[635,7]) ).
tff(637,plain,
sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x12,x7),sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(symmetry,[status(thm)],[636]) ).
tff(638,plain,
sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))),
inference(monotonicity,[status(thm)],[10]) ).
tff(639,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))) = sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))),
inference(symmetry,[status(thm)],[638]) ).
tff(640,plain,
sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(monotonicity,[status(thm)],[639]) ).
tff(641,plain,
sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(symmetry,[status(thm)],[640]) ).
tff(642,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(643,plain,
sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(unit_resolution,[status(thm)],[642,7]) ).
tff(644,plain,
sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[643]) ).
tff(645,plain,
sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(transitivity,[status(thm)],[644,641]) ).
tff(646,plain,
sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[645]) ).
tff(647,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[646]) ).
tff(648,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(649,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[648,7]) ).
tff(650,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[649]) ).
tff(651,plain,
sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[645]) ).
tff(652,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[651]) ).
tff(653,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[652]) ).
tff(654,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[653,650,647]) ).
tff(655,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[654]) ).
tff(656,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(657,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[656,7]) ).
tff(658,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[652]) ).
tff(659,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[658]) ).
tff(660,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(661,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[660,7]) ).
tff(662,plain,
sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[661]) ).
tff(663,plain,
sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[662,659]) ).
tff(664,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[663]) ).
tff(665,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(666,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[665,7]) ).
tff(667,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[666]) ).
tff(668,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[667,664,657,655]) ).
tff(669,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[668]) ).
tff(670,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(671,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[670,7]) ).
tff(672,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[646]) ).
tff(673,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[672]) ).
tff(674,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[673]) ).
tff(675,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(676,plain,
sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[675,7]) ).
tff(677,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[676]) ).
tff(678,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[677,674]) ).
tff(679,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[678]) ).
tff(680,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[679]) ).
tff(681,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[680]) ).
tff(682,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(683,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[682,7]) ).
tff(684,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[683]) ).
tff(685,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[684,679]) ).
tff(686,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[685]) ).
tff(687,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(688,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[687,7]) ).
tff(689,plain,
sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[688]) ).
tff(690,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(691,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[690,7]) ).
tff(692,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[663]) ).
tff(693,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[692]) ).
tff(694,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(695,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[694,7]) ).
tff(696,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[695]) ).
tff(697,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[696,693,691]) ).
tff(698,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[697]) ).
tff(699,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[698,689,686,681,671,669]) ).
tff(700,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[699]) ).
tff(701,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(702,plain,
sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[701,7]) ).
tff(703,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x1),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(704,plain,
sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x1),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[703,7]) ).
tff(705,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))) = sep(lseg(x11,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(706,plain,
sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))) = sep(lseg(x11,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))),
inference(unit_resolution,[status(thm)],[705,7]) ).
tff(707,plain,
sep(lseg(x11,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))) = sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))),
inference(symmetry,[status(thm)],[706]) ).
tff(708,plain,
sep(lseg(x11,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))),
inference(transitivity,[status(thm)],[707,638]) ).
tff(709,plain,
sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(monotonicity,[status(thm)],[708]) ).
tff(710,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))) = sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(711,plain,
sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))) = sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))),
inference(unit_resolution,[status(thm)],[710,7]) ).
tff(712,plain,
sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[711]) ).
tff(713,plain,
sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(transitivity,[status(thm)],[712,709]) ).
tff(714,plain,
sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[713]) ).
tff(715,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[714]) ).
tff(716,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x11,x1),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[715,704]) ).
tff(717,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[716]) ).
tff(718,plain,
sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[717]) ).
tff(719,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(720,plain,
sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[719,7]) ).
tff(721,plain,
sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[720]) ).
tff(722,plain,
sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[721,718]) ).
tff(723,plain,
sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[722]) ).
tff(724,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[723]) ).
tff(725,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[724]) ).
tff(726,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(728,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[727,7]) ).
tff(729,plain,
sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[722]) ).
tff(730,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[729]) ).
tff(731,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[730]) ).
tff(732,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[731,728,726]) ).
tff(733,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[732]) ).
tff(734,plain,
sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))) = sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))),
inference(monotonicity,[status(thm)],[52]) ).
tff(735,plain,
sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(transitivity,[status(thm)],[734,644,641]) ).
tff(736,plain,
sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[735]) ).
tff(737,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(738,plain,
sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[737,7]) ).
tff(739,plain,
sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x7,x10),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[738]) ).
tff(740,plain,
sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[411]) ).
tff(741,plain,
sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[420]) ).
tff(742,plain,
sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(transitivity,[status(thm)],[741,740,739,736]) ).
tff(743,plain,
sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[742]) ).
tff(744,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(745,plain,
sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[744,7]) ).
tff(746,plain,
sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[745]) ).
tff(747,plain,
sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[422]) ).
tff(748,plain,
sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[417]) ).
tff(749,plain,
sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[748,747,746,743]) ).
tff(750,plain,
sep(lseg(x5,x3),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[749]) ).
tff(751,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(752,plain,
sep(lseg(x5,x3),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[751,7]) ).
tff(753,plain,
sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[752]) ).
tff(754,plain,
sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[753,750]) ).
tff(755,plain,
sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[754]) ).
tff(756,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(757,plain,
sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[756,7]) ).
tff(758,plain,
sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[757]) ).
tff(759,plain,
sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[758,755]) ).
tff(760,plain,
sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[759]) ).
tff(761,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(762,plain,
sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[761,7]) ).
tff(763,plain,
sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[762]) ).
tff(764,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[472]) ).
tff(765,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[764]) ).
tff(766,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(767,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[766,7]) ).
tff(768,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[767]) ).
tff(769,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[768,765]) ).
tff(770,plain,
sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[769]) ).
tff(771,plain,
sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[770]) ).
tff(772,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[422]) ).
tff(773,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[772]) ).
tff(774,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(775,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[774,7]) ).
tff(776,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[775]) ).
tff(777,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[776,773]) ).
tff(778,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[777]) ).
tff(779,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[778]) ).
tff(780,plain,
sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[779]) ).
tff(781,plain,
sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[780]) ).
tff(782,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(783,plain,
sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[782,7]) ).
tff(784,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[783]) ).
tff(785,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[777]) ).
tff(786,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[785]) ).
tff(787,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[786]) ).
tff(788,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[787,784,781,771]) ).
tff(789,plain,
sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[788]) ).
tff(790,plain,
sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[789,763,760,733,702,700]) ).
tff(791,plain,
sep(lseg(x10,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[790]) ).
tff(792,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(793,plain,
sep(lseg(x10,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[792,7]) ).
tff(794,plain,
sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[793]) ).
tff(795,plain,
sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[794,791]) ).
tff(796,plain,
sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[795]) ).
tff(797,plain,
sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(monotonicity,[status(thm)],[796]) ).
tff(798,plain,
sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(transitivity,[status(thm)],[797,637,634,535,532,491]) ).
tff(799,plain,
( heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))))
<=> heap(sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))))) ),
inference(monotonicity,[status(thm)],[798]) ).
tff(800,plain,
( heap(sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))))
<=> heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) ),
inference(symmetry,[status(thm)],[799]) ).
tff(801,plain,
( heap(sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))))
<=> heap(sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(802,axiom,
heap(sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_13) ).
tff(803,plain,
heap(sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))))),
inference(modus_ponens,[status(thm)],[802,801]) ).
tff(804,plain,
heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))),
inference(modus_ponens,[status(thm)],[803,800]) ).
tff(805,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[791]) ).
tff(806,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(807,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))),
inference(unit_resolution,[status(thm)],[806,7]) ).
tff(808,plain,
sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))),
inference(symmetry,[status(thm)],[807]) ).
tff(809,plain,
sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(monotonicity,[status(thm)],[808]) ).
tff(810,plain,
sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))),
inference(symmetry,[status(thm)],[809]) ).
tff(811,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[810]) ).
tff(812,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[811]) ).
tff(813,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(814,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))),
inference(unit_resolution,[status(thm)],[813,7]) ).
tff(815,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[814]) ).
tff(816,plain,
sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(transitivity,[status(thm)],[815,812]) ).
tff(817,plain,
sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))) = sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[816]) ).
tff(818,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[817]) ).
tff(819,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(820,plain,
sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[819,7]) ).
tff(821,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[820]) ).
tff(822,plain,
sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[816]) ).
tff(823,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[822]) ).
tff(824,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[823]) ).
tff(825,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x1),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(826,plain,
sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x1),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[825,7]) ).
tff(827,plain,
sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[713]) ).
tff(828,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[827]) ).
tff(829,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x11,x1),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[828,826]) ).
tff(830,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[829]) ).
tff(831,plain,
sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[830]) ).
tff(832,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(833,plain,
sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[832,7]) ).
tff(834,plain,
sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x11,x1),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[833]) ).
tff(835,plain,
sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[834,831]) ).
tff(836,plain,
sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[835]) ).
tff(837,plain,
sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[836,824,821,818]) ).
tff(838,plain,
sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[837]) ).
tff(839,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(840,plain,
sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[839,7]) ).
tff(841,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[840]) ).
tff(842,plain,
sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[835]) ).
tff(843,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[842]) ).
tff(844,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[823]) ).
tff(845,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[844]) ).
tff(846,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(847,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[846,7]) ).
tff(848,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[847]) ).
tff(849,plain,
sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))),
inference(transitivity,[status(thm)],[811,814]) ).
tff(850,plain,
sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[849]) ).
tff(851,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[850]) ).
tff(852,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[851]) ).
tff(853,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[852]) ).
tff(854,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[853,848,845,843]) ).
tff(855,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[854]) ).
tff(856,plain,
sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[855,841,838,681,671,669]) ).
tff(857,plain,
sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[856]) ).
tff(858,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(859,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[858,7]) ).
tff(860,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[859,857]) ).
tff(861,plain,
sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[860]) ).
tff(862,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(863,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[862,7]) ).
tff(864,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(865,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[864,7]) ).
tff(866,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[865]) ).
tff(867,plain,
sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[835]) ).
tff(868,plain,
sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[867]) ).
tff(869,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(870,plain,
sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[869,7]) ).
tff(871,plain,
sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[870]) ).
tff(872,plain,
sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[854]) ).
tff(873,plain,
sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[872,871,868]) ).
tff(874,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[873]) ).
tff(875,plain,
sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[874]) ).
tff(876,plain,
sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[875,866]) ).
tff(877,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[876]) ).
tff(878,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[654]) ).
tff(879,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(880,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[879,7]) ).
tff(881,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[880]) ).
tff(882,plain,
sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[722]) ).
tff(883,plain,
sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[882,881,878]) ).
tff(884,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[883]) ).
tff(885,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(886,plain,
sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[885,7]) ).
tff(887,plain,
sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[730]) ).
tff(888,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(889,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[888,7]) ).
tff(890,plain,
sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[889]) ).
tff(891,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[890]) ).
tff(892,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(893,plain,
sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[892,7]) ).
tff(894,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x4,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[893]) ).
tff(895,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(896,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[895,7]) ).
tff(897,plain,
sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[654]) ).
tff(898,plain,
sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[897]) ).
tff(899,plain,
sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[898,896]) ).
tff(900,plain,
sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[899]) ).
tff(901,plain,
sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[851]) ).
tff(902,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(903,plain,
sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[902,7]) ).
tff(904,plain,
sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[903]) ).
tff(905,plain,
sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[904,901]) ).
tff(906,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[905]) ).
tff(907,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(908,plain,
sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[907,7]) ).
tff(909,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[908]) ).
tff(910,plain,
sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[909,906,900,894,891,887,886,884]) ).
tff(911,plain,
sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[910]) ).
tff(912,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(913,plain,
sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x2,x9),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[912,7]) ).
tff(914,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[823]) ).
tff(915,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[914]) ).
tff(916,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(917,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[916,7]) ).
tff(918,plain,
sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[917]) ).
tff(919,plain,
sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[918,915]) ).
tff(920,plain,
sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[919]) ).
tff(921,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[920]) ).
tff(922,plain,
sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x5,x3),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[921]) ).
tff(923,plain,
sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[835]) ).
tff(924,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[923]) ).
tff(925,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[924]) ).
tff(926,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[925]) ).
tff(927,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(928,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[927,7]) ).
tff(929,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[928]) ).
tff(930,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[929,926]) ).
tff(931,plain,
sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[930]) ).
tff(932,plain,
sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[931,922,913,911,865,874]) ).
tff(933,plain,
sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x2,x9),sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[932]) ).
tff(934,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(935,plain,
sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x2,x9),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[934,7]) ).
tff(936,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[930]) ).
tff(937,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[936]) ).
tff(938,plain,
sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x1),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[937]) ).
tff(939,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))) = sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(940,plain,
sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))) = sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))),
inference(unit_resolution,[status(thm)],[939,7]) ).
tff(941,plain,
sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))),
inference(symmetry,[status(thm)],[940]) ).
tff(942,plain,
sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))),
inference(transitivity,[status(thm)],[941,809]) ).
tff(943,plain,
sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[942]) ).
tff(944,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(945,plain,
sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))),
inference(unit_resolution,[status(thm)],[944,7]) ).
tff(946,plain,
sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[945]) ).
tff(947,plain,
sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(transitivity,[status(thm)],[946,943]) ).
tff(948,plain,
sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[947]) ).
tff(949,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))) = sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(950,plain,
sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))) = sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[949,7]) ).
tff(951,plain,
sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[950]) ).
tff(952,plain,
sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[951,948]) ).
tff(953,plain,
sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[952]) ).
tff(954,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(955,plain,
sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[954,7]) ).
tff(956,plain,
sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[955]) ).
tff(957,plain,
sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[956,953]) ).
tff(958,plain,
sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[957]) ).
tff(959,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(960,plain,
sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[959,7]) ).
tff(961,plain,
sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[960]) ).
tff(962,plain,
sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[961,958]) ).
tff(963,plain,
sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[962]) ).
tff(964,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(965,plain,
sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[964,7]) ).
tff(966,plain,
sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[965]) ).
tff(967,plain,
sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[966,963]) ).
tff(968,plain,
sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[967]) ).
tff(969,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(970,plain,
sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[969,7]) ).
tff(971,plain,
sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x2,x9),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[970]) ).
tff(972,plain,
sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[971,968,938,935,933,877,863,861,805,793]) ).
tff(973,plain,
sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[972]) ).
tff(974,plain,
( heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))))))
<=> heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[973]) ).
tff(975,plain,
( ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp))))))))))))
<=> ~ heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[974]) ).
tff(976,plain,
( ( x11 = x7 )
<=> ( x7 = x11 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(977,plain,
( ( x7 = x11 )
<=> ( x11 = x7 ) ),
inference(symmetry,[status(thm)],[976]) ).
tff(978,plain,
( ( x7 != x11 )
<=> ( x11 != x7 ) ),
inference(monotonicity,[status(thm)],[977]) ).
tff(979,plain,
( ( x7 != x11 )
<=> ( x7 != x11 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(980,axiom,
x7 != x11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_7) ).
tff(981,plain,
x7 != x11,
inference(modus_ponens,[status(thm)],[980,979]) ).
tff(982,plain,
x11 != x7,
inference(modus_ponens,[status(thm)],[981,978]) ).
tff(983,plain,
^ [Sigma: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
<=> ( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ) )),
inference(bind,[status(th)],[]) ).
tff(984,plain,
( ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
<=> ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ) ),
inference(quant_intro,[status(thm)],[983]) ).
tff(985,plain,
( ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
<=> ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(986,plain,
^ [Sigma: $i,Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma)))
| ( X = Y )
| ( X = Z ) )
<=> ( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ) )),
inference(bind,[status(th)],[]) ).
tff(987,plain,
( ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma)))
| ( X = Y )
| ( X = Z ) )
<=> ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ) ),
inference(quant_intro,[status(thm)],[986]) ).
tff(988,axiom,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma)))
| ( X = Y )
| ( X = Z ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',wellformedness_5) ).
tff(989,plain,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ),
inference(modus_ponens,[status(thm)],[988,987]) ).
tff(990,plain,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ),
inference(modus_ponens,[status(thm)],[989,985]) ).
tff(991,plain,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ),
inference(skolemize,[status(sab)],[990]) ).
tff(992,plain,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ),
inference(modus_ponens,[status(thm)],[991,984]) ).
tff(993,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(994,plain,
( ( ( x11 = x7 )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) )
<=> ( ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(995,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) ) ),
inference(monotonicity,[status(thm)],[994]) ).
tff(996,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) ) ),
inference(transitivity,[status(thm)],[995,993]) ).
tff(997,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(998,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[997,996]) ).
tff(999,plain,
~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x1),emp)))))))))))),
inference(unit_resolution,[status(thm)],[998,992,982]) ).
tff(1000,plain,
~ heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))),
inference(modus_ponens,[status(thm)],[999,975]) ).
tff(1001,plain,
^ [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
<=> ( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) )),
inference(bind,[status(th)],[]) ).
tff(1002,plain,
( ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
<=> ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) ),
inference(quant_intro,[status(thm)],[1001]) ).
tff(1003,plain,
( ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
<=> ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1004,plain,
^ [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma))))
| ( Z = W )
| heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma))) )
<=> ( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) )),
inference(bind,[status(th)],[]) ).
tff(1005,plain,
( ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma))))
| ( Z = W )
| heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma))) )
<=> ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) ),
inference(quant_intro,[status(thm)],[1004]) ).
tff(1006,axiom,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma))))
| ( Z = W )
| heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',unfolding_5) ).
tff(1007,plain,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ),
inference(modus_ponens,[status(thm)],[1006,1005]) ).
tff(1008,plain,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ),
inference(modus_ponens,[status(thm)],[1007,1003]) ).
tff(1009,plain,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ),
inference(skolemize,[status(sab)],[1008]) ).
tff(1010,plain,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ),
inference(modus_ponens,[status(thm)],[1009,1002]) ).
tff(1011,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x10 )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x10 )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1012,plain,
( ( heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ( x7 = x10 )
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) )
<=> ( ( x7 = x10 )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1013,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ( x7 = x10 )
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x10 )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(monotonicity,[status(thm)],[1012]) ).
tff(1014,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ( x7 = x10 )
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x10 )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(transitivity,[status(thm)],[1013,1011]) ).
tff(1015,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ( x7 = x10 )
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1016,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x10 )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) ),
inference(modus_ponens,[status(thm)],[1015,1014]) ).
tff(1017,plain,
( ( x7 = x10 )
| heap(sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))) ),
inference(unit_resolution,[status(thm)],[1016,1010]) ).
tff(1018,plain,
x7 = x10,
inference(unit_resolution,[status(thm)],[1017,1000,804]) ).
tff(1019,plain,
lseg(x12,x7) = lseg(x12,x10),
inference(monotonicity,[status(thm)],[1018]) ).
tff(1020,plain,
lseg(x12,x10) = lseg(x12,x7),
inference(symmetry,[status(thm)],[1019]) ).
tff(1021,plain,
sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[1020]) ).
tff(1022,plain,
sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[1021,488,486]) ).
tff(1023,plain,
sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x11,x12),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[1022]) ).
tff(1024,plain,
sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[1023,376,373,357,347,344,323,321,244,234,232,173]) ).
tff(1025,plain,
( heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
<=> heap(sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[1024]) ).
tff(1026,plain,
( heap(sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))))
<=> heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ),
inference(symmetry,[status(thm)],[1025]) ).
tff(1027,plain,
sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[1020]) ).
tff(1028,plain,
sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[1027,344,323,321,244,234,232,173]) ).
tff(1029,plain,
( heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
<=> heap(sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[1028]) ).
tff(1030,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))),
inference(monotonicity,[status(thm)],[178]) ).
tff(1031,plain,
sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[1030]) ).
tff(1032,plain,
sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(monotonicity,[status(thm)],[1031]) ).
tff(1033,plain,
sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))) = sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))),
inference(transitivity,[status(thm)],[1032,558,555]) ).
tff(1034,plain,
sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(monotonicity,[status(thm)],[1033]) ).
tff(1035,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1036,plain,
sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[1035,7]) ).
tff(1037,plain,
sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x7,x10),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[1036]) ).
tff(1038,plain,
sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))),
inference(transitivity,[status(thm)],[1037,1034]) ).
tff(1039,plain,
sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[1038]) ).
tff(1040,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1041,plain,
sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[1040,7]) ).
tff(1042,plain,
sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x7,x10),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[1041]) ).
tff(1043,plain,
sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))),
inference(transitivity,[status(thm)],[1042,1039]) ).
tff(1044,plain,
sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(monotonicity,[status(thm)],[1043]) ).
tff(1045,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1046,plain,
sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[1045,7]) ).
tff(1047,plain,
sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x7,x10),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[1046]) ).
tff(1048,plain,
sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[1047,1044]) ).
tff(1049,plain,
sep(lseg(x5,x3),sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[1048]) ).
tff(1050,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1051,plain,
sep(lseg(x5,x3),sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(unit_resolution,[status(thm)],[1050,7]) ).
tff(1052,plain,
sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x5,x3),sep(lseg(x7,x10),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))),
inference(symmetry,[status(thm)],[1051]) ).
tff(1053,plain,
sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))),
inference(transitivity,[status(thm)],[1052,1049]) ).
tff(1054,plain,
sep(lseg(x10,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(monotonicity,[status(thm)],[1053]) ).
tff(1055,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1056,plain,
sep(lseg(x10,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(unit_resolution,[status(thm)],[1055,7]) ).
tff(1057,plain,
sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x7,x10),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))),
inference(symmetry,[status(thm)],[1056]) ).
tff(1058,plain,
sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))),
inference(transitivity,[status(thm)],[1057,1054]) ).
tff(1059,plain,
sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x12,x7),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(monotonicity,[status(thm)],[1058]) ).
tff(1060,plain,
sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))),
inference(transitivity,[status(thm)],[1059,535,532,491]) ).
tff(1061,plain,
( heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))))))
<=> heap(sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp))))))))))))) ),
inference(monotonicity,[status(thm)],[1060]) ).
tff(1062,plain,
( heap(sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x12,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x12),sep(lseg(x11,x7),sep(lseg(x11,x1),emp)))))))))))))
<=> heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) ),
inference(symmetry,[status(thm)],[1061]) ).
tff(1063,plain,
heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))),
inference(modus_ponens,[status(thm)],[803,1062]) ).
tff(1064,plain,
( ( x7 = x8 )
<=> ( x10 = x8 ) ),
inference(monotonicity,[status(thm)],[1018]) ).
tff(1065,plain,
( ( x7 != x8 )
<=> ( x10 != x8 ) ),
inference(monotonicity,[status(thm)],[1064]) ).
tff(1066,plain,
( ( x7 != x8 )
<=> ( x7 != x8 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1067,axiom,
x7 != x8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_6) ).
tff(1068,plain,
x7 != x8,
inference(modus_ponens,[status(thm)],[1067,1066]) ).
tff(1069,plain,
x10 != x8,
inference(modus_ponens,[status(thm)],[1068,1065]) ).
tff(1070,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1071,plain,
( ( heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ( x10 = x8 )
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) )
<=> ( ( x10 = x8 )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1072,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ( x10 = x8 )
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) ) ),
inference(monotonicity,[status(thm)],[1071]) ).
tff(1073,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ( x10 = x8 )
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) ) ),
inference(transitivity,[status(thm)],[1072,1070]) ).
tff(1074,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ( x10 = x8 )
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1075,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) ),
inference(modus_ponens,[status(thm)],[1074,1073]) ).
tff(1076,plain,
( ( x10 = x8 )
| heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))
| ~ heap(sep(lseg(x12,x7),sep(lseg(x7,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp))))))))))))) ),
inference(unit_resolution,[status(thm)],[1075,1010]) ).
tff(1077,plain,
heap(sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x7),sep(lseg(x11,x12),sep(lseg(x11,x1),emp)))))))))))),
inference(unit_resolution,[status(thm)],[1076,1069,1063]) ).
tff(1078,plain,
heap(sep(lseg(x1,x11),sep(lseg(x11,x12),sep(lseg(x12,x7),sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x4,x9),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))),
inference(modus_ponens,[status(thm)],[1077,1029]) ).
tff(1079,plain,
heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))),
inference(modus_ponens,[status(thm)],[1078,1026]) ).
tff(1080,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1081,plain,
sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))),
inference(unit_resolution,[status(thm)],[1080,7]) ).
tff(1082,plain,
sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x11,x7),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))),
inference(symmetry,[status(thm)],[433]) ).
tff(1083,plain,
sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))) = sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[1082,444]) ).
tff(1084,plain,
sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[1083]) ).
tff(1085,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1086,plain,
sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))),
inference(unit_resolution,[status(thm)],[1085,7]) ).
tff(1087,plain,
sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))),
inference(symmetry,[status(thm)],[1086]) ).
tff(1088,plain,
sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))) = sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[1087,1084]) ).
tff(1089,plain,
sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[1088]) ).
tff(1090,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1091,plain,
sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))),
inference(unit_resolution,[status(thm)],[1090,7]) ).
tff(1092,plain,
sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x11,x7),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))),
inference(symmetry,[status(thm)],[1091]) ).
tff(1093,plain,
sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[1092,1089]) ).
tff(1094,plain,
sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[1093]) ).
tff(1095,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1096,plain,
sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[1095,7]) ).
tff(1097,plain,
sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[1096]) ).
tff(1098,plain,
sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[1097,1094]) ).
tff(1099,plain,
sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[1098]) ).
tff(1100,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))),
inference(symmetry,[status(thm)],[1099]) ).
tff(1101,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(monotonicity,[status(thm)],[460]) ).
tff(1102,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[1101]) ).
tff(1103,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1104,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(unit_resolution,[status(thm)],[1103,7]) ).
tff(1105,plain,
sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[140]) ).
tff(1106,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1107,plain,
sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[1106,7]) ).
tff(1108,plain,
sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[1107]) ).
tff(1109,plain,
sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[139]) ).
tff(1110,plain,
sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[1109]) ).
tff(1111,plain,
sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x9,x2),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[1110]) ).
tff(1112,plain,
sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x10,x8),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[452]) ).
tff(1113,plain,
sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))) = sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[1112,1111,1108,1105]) ).
tff(1114,plain,
sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[1113]) ).
tff(1115,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x10,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[1114]) ).
tff(1116,plain,
sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[1115,1104,1102]) ).
tff(1117,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[1116]) ).
tff(1118,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[1117]) ).
tff(1119,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1120,plain,
sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[1119,7]) ).
tff(1121,plain,
sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[1120]) ).
tff(1122,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x13,x8),sep(lseg(x11,x7),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))),
inference(symmetry,[status(thm)],[470]) ).
tff(1123,plain,
sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[467,1122,481]) ).
tff(1124,plain,
sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[1123]) ).
tff(1125,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x8),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[1124]) ).
tff(1126,plain,
sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))),
inference(transitivity,[status(thm)],[1125,1121,1118,1100,1081]) ).
tff(1127,plain,
lseg(x11,x7) = lseg(x11,x10),
inference(monotonicity,[status(thm)],[1018]) ).
tff(1128,plain,
lseg(x11,x10) = lseg(x11,x7),
inference(symmetry,[status(thm)],[1127]) ).
tff(1129,plain,
sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))))),
inference(monotonicity,[status(thm)],[1128,1126]) ).
tff(1130,plain,
( heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
<=> heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) ),
inference(monotonicity,[status(thm)],[1129]) ).
tff(1131,plain,
( heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))))))
<=> heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) ),
inference(symmetry,[status(thm)],[1130]) ).
tff(1132,plain,
( ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp)))))))))))
<=> ~ heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))) ),
inference(monotonicity,[status(thm)],[1131]) ).
tff(1133,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1134,plain,
( ( ( x11 = x7 )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) )
<=> ( ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1135,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(monotonicity,[status(thm)],[1134]) ).
tff(1136,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) ) ),
inference(transitivity,[status(thm)],[1135,1133]) ).
tff(1137,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1138,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[1137,1136]) ).
tff(1139,plain,
~ heap(sep(lseg(x11,x7),sep(lseg(x11,x7),sep(lseg(x13,x8),sep(lseg(x5,x3),sep(lseg(x1,x11),sep(lseg(x10,x8),sep(lseg(x4,x9),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),emp))))))))))),
inference(unit_resolution,[status(thm)],[1138,992,982]) ).
tff(1140,plain,
~ heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp))))))))))),
inference(modus_ponens,[status(thm)],[1139,1132]) ).
tff(1141,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1142,plain,
( ( heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ( x10 = x8 )
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) )
<=> ( ( x10 = x8 )
| heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1143,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ( x10 = x8 )
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(monotonicity,[status(thm)],[1142]) ).
tff(1144,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ( x10 = x8 )
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(transitivity,[status(thm)],[1143,1141]) ).
tff(1145,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ( x10 = x8 )
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1146,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x10 = x8 )
| heap(sep(lseg(x11,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))
| ~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[1145,1144]) ).
tff(1147,plain,
~ heap(sep(lseg(x11,x12),sep(lseg(x12,x10),sep(lseg(x10,x8),sep(lseg(x5,x3),sep(lseg(x4,x9),sep(lseg(x13,x8),sep(lseg(x1,x11),sep(lseg(x2,x9),sep(lseg(x9,x2),sep(lseg(x11,x1),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[1146,1010,1069,1140]) ).
tff(1148,plain,
$false,
inference(unit_resolution,[status(thm)],[1147,1079]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW431-1 : TPTP v9.0.0. Released v5.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 11:42:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 36.24/36.42 % SZS status Unsatisfiable
% 36.24/36.42 % SZS output start Proof
% See solution above
% 36.63/36.85 % E exiting
%------------------------------------------------------------------------------