%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW438-1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:37:00 AM UTC 2025
% Result : Unsatisfiable 11.14s 11.32s
% Output : Proof 11.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 182
% Syntax : Number of formulae : 976 ( 763 unt; 0 typ; 0 def)
% Number of atoms : 1361 (1241 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 656 ( 275 ~; 336 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of FOOLs : 4 ( 4 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 : 661 ( 648 !; 0 ?; 661 :)
% 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(x14_type,type,
x14: $i ).
tff(x6_type,type,
x6: $i ).
tff(x3_type,type,
x3: $i ).
tff(x16_type,type,
x16: $i ).
tff(x7_type,type,
x7: $i ).
tff(x4_type,type,
x4: $i ).
tff(x11_type,type,
x11: $i ).
tff(x2_type,type,
x2: $i ).
tff(x8_type,type,
x8: $i ).
tff(x13_type,type,
x13: $i ).
tff(x12_type,type,
x12: $i ).
tff(x10_type,type,
x10: $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/sandbox/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(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[15,7]) ).
tff(17,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[17,14]) ).
tff(19,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),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(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[28,7]) ).
tff(30,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[30,27]) ).
tff(32,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),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(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[35,32]) ).
tff(37,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[37,7]) ).
tff(39,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(unit_resolution,[status(thm)],[39,7]) ).
tff(41,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(unit_resolution,[status(thm)],[45,7]) ).
tff(47,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))) = sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))) = sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))),
inference(unit_resolution,[status(thm)],[48,7]) ).
tff(50,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))) = sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(transitivity,[status(thm)],[53,47,44,40]) ).
tff(55,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(transitivity,[status(thm)],[58,55]) ).
tff(60,plain,
sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[61,7]) ).
tff(63,plain,
sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[63,60]) ).
tff(65,plain,
sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[66,7]) ).
tff(68,plain,
sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[68,65]) ).
tff(70,plain,
sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[71,7]) ).
tff(73,plain,
sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[73,70]) ).
tff(75,plain,
sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(symmetry,[status(thm)],[44]) ).
tff(78,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(symmetry,[status(thm)],[40]) ).
tff(79,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(transitivity,[status(thm)],[78,77]) ).
tff(80,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(unit_resolution,[status(thm)],[82,7]) ).
tff(84,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(transitivity,[status(thm)],[84,81]) ).
tff(86,plain,
sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[90,7]) ).
tff(92,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[92,89]) ).
tff(94,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[98,7]) ).
tff(100,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[100,7]) ).
tff(102,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[85]) ).
tff(103,plain,
sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),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(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[104,7]) ).
tff(106,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(monotonicity,[status(thm)],[78]) ).
tff(107,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[108,105,103]) ).
tff(110,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[110,101]) ).
tff(112,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[114,7]) ).
tff(116,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[116,113]) ).
tff(118,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[108]) ).
tff(121,plain,
sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[105]) ).
tff(122,plain,
sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[121,120]) ).
tff(123,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[127,7]) ).
tff(129,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[122]) ).
tff(130,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[131,128,126]) ).
tff(133,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[135,7]) ).
tff(137,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[122]) ).
tff(139,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[140,7]) ).
tff(142,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[124]) ).
tff(144,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[143,142,139]) ).
tff(145,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(transitivity,[status(thm)],[53,47,44]) ).
tff(148,plain,
sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))),
inference(unit_resolution,[status(thm)],[149,7]) ).
tff(151,plain,
sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(transitivity,[status(thm)],[151,148]) ).
tff(153,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[154,7]) ).
tff(156,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[156,153]) ).
tff(158,plain,
sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[159,7]) ).
tff(161,plain,
sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[161,158]) ).
tff(163,plain,
sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[164,7]) ).
tff(166,plain,
sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[166,163]) ).
tff(168,plain,
sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[169,7]) ).
tff(171,plain,
sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[171,168,146,137,134,119,99,97,76,38]) ).
tff(173,plain,
sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[175,7]) ).
tff(177,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[178,7]) ).
tff(180,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(unit_resolution,[status(thm)],[180,7]) ).
tff(182,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(transitivity,[status(thm)],[182,106]) ).
tff(184,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[186,7]) ).
tff(188,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[188,185]) ).
tff(190,plain,
sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[129]) ).
tff(193,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[193,7]) ).
tff(195,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[138]) ).
tff(197,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[197,195,192,191,179]) ).
tff(199,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[200,177,146,137,134,119,99,97,76,38]) ).
tff(202,plain,
sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))),
inference(transitivity,[status(thm)],[202,174]) ).
tff(204,plain,
( heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))))) ),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
( heap(sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(207,plain,
sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[206,7]) ).
tff(208,plain,
sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[211,7]) ).
tff(213,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[25]) ).
tff(215,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[215,7]) ).
tff(217,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[217,214,207]) ).
tff(219,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[220,7]) ).
tff(222,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[222,219]) ).
tff(224,plain,
sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[225,7]) ).
tff(227,plain,
sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[226]) ).
tff(228,plain,
sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[227,224,213,210]) ).
tff(229,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(231,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(unit_resolution,[status(thm)],[230,7]) ).
tff(232,plain,
sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[191,179]) ).
tff(234,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[99]) ).
tff(237,plain,
sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[38]) ).
tff(238,plain,
sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[237,75,96,236,118,133,136,145,176,199,235]) ).
tff(239,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[239,7]) ).
tff(241,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[207]) ).
tff(243,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[244,7]) ).
tff(246,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(unit_resolution,[status(thm)],[247,7]) ).
tff(249,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[252,246,243]) ).
tff(254,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(256,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[255,7]) ).
tff(257,plain,
sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[257,254,241]) ).
tff(259,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(unit_resolution,[status(thm)],[260,7]) ).
tff(262,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(264,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[263,7]) ).
tff(265,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(monotonicity,[status(thm)],[78]) ).
tff(266,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(268,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[267,7]) ).
tff(269,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[268]) ).
tff(270,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[269,266,249]) ).
tff(271,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[270]) ).
tff(272,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(273,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[272,7]) ).
tff(274,plain,
sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[274,271]) ).
tff(276,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[275]) ).
tff(277,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(278,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[277,7]) ).
tff(279,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[279,276]) ).
tff(281,plain,
sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[280]) ).
tff(282,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(283,plain,
sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[282,7]) ).
tff(284,plain,
sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[283]) ).
tff(285,plain,
sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[284,281,264]) ).
tff(286,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(transitivity,[status(thm)],[286,262,259]) ).
tff(288,plain,
( heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
( heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
( heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(291,axiom,
heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_16) ).
tff(292,plain,
heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))),
inference(modus_ponens,[status(thm)],[291,290]) ).
tff(293,plain,
heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))),
inference(modus_ponens,[status(thm)],[292,289]) ).
tff(294,plain,
( ( x10 = x3 )
<=> ( x3 = x10 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(295,plain,
( ( x3 = x10 )
<=> ( x10 = x3 ) ),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( ( x3 != x10 )
<=> ( x10 != x3 ) ),
inference(monotonicity,[status(thm)],[295]) ).
tff(297,plain,
( ( x3 != x10 )
<=> ( x3 != x10 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(298,axiom,
x3 != x10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).
tff(299,plain,
x3 != x10,
inference(modus_ponens,[status(thm)],[298,297]) ).
tff(300,plain,
x10 != x3,
inference(modus_ponens,[status(thm)],[299,296]) ).
tff(301,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(302,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)],[301]) ).
tff(303,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(304,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(305,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)],[304]) ).
tff(306,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/sandbox/benchmark/Axioms/SWV013-0.ax',wellformedness_5) ).
tff(307,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)],[306,305]) ).
tff(308,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)],[307,303]) ).
tff(309,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)],[308]) ).
tff(310,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)],[309,302]) ).
tff(311,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x10 = x2 )
| ( x10 = x3 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x10 = x2 )
| ( x10 = x3 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(312,plain,
( ( ( x10 = x3 )
| ( x10 = x2 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) )
<=> ( ( x10 = x2 )
| ( x10 = x3 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(313,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x10 = x3 )
| ( x10 = x2 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x10 = x2 )
| ( x10 = x3 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ) ),
inference(monotonicity,[status(thm)],[312]) ).
tff(314,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x10 = x3 )
| ( x10 = x2 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x10 = x2 )
| ( x10 = x3 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ) ),
inference(transitivity,[status(thm)],[313,311]) ).
tff(315,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x10 = x3 )
| ( x10 = x2 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(316,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x10 = x2 )
| ( x10 = x3 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(modus_ponens,[status(thm)],[315,314]) ).
tff(317,plain,
( ( x10 = x2 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(unit_resolution,[status(thm)],[316,310,300]) ).
tff(318,plain,
x10 = x2,
inference(unit_resolution,[status(thm)],[317,293]) ).
tff(319,plain,
x2 = x10,
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
lseg(x2,x3) = lseg(x10,x3),
inference(monotonicity,[status(thm)],[319]) ).
tff(321,plain,
sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[320,238]) ).
tff(322,plain,
sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(transitivity,[status(thm)],[173,321,232,229,10]) ).
tff(323,plain,
( heap(sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(monotonicity,[status(thm)],[322]) ).
tff(324,plain,
( heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x2,x3),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))))) ),
inference(symmetry,[status(thm)],[323]) ).
tff(325,plain,
( heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(transitivity,[status(thm)],[324,205]) ).
tff(326,plain,
heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))),
inference(modus_ponens,[status(thm)],[292,325]) ).
tff(327,plain,
( ( x2 = x3 )
<=> ( x10 = x3 ) ),
inference(monotonicity,[status(thm)],[319]) ).
tff(328,plain,
( ( x2 = x3 )
<=> ( x3 = x10 ) ),
inference(transitivity,[status(thm)],[327,294]) ).
tff(329,plain,
( ( x3 = x10 )
<=> ( x2 = x3 ) ),
inference(symmetry,[status(thm)],[328]) ).
tff(330,plain,
( ( x3 != x10 )
<=> ( x2 != x3 ) ),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
x2 != x3,
inference(modus_ponens,[status(thm)],[299,330]) ).
tff(332,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x13 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x13 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(333,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x13 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(334,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x13 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(modus_ponens,[status(thm)],[333,332]) ).
tff(335,plain,
( ( x2 = x13 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(unit_resolution,[status(thm)],[334,310]) ).
tff(336,plain,
x2 = x13,
inference(unit_resolution,[status(thm)],[335,331,326]) ).
tff(337,plain,
lseg(x2,x8) = lseg(x13,x8),
inference(monotonicity,[status(thm)],[336]) ).
tff(338,plain,
sep(lseg(x2,x8),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[337,36]) ).
tff(339,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[32]) ).
tff(340,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(341,plain,
sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[340,7]) ).
tff(342,plain,
sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[341]) ).
tff(343,plain,
sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[342,26]) ).
tff(344,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[343]) ).
tff(345,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(346,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[345,7]) ).
tff(347,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[347,344]) ).
tff(349,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[348]) ).
tff(350,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(351,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[350,7]) ).
tff(352,plain,
sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[351]) ).
tff(353,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(354,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[353,7]) ).
tff(355,plain,
sep(lseg(x13,x6),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[183]) ).
tff(356,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[355]) ).
tff(357,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[357,354]) ).
tff(359,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[358]) ).
tff(360,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(362,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[361,7]) ).
tff(363,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[362]) ).
tff(364,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[363,360]) ).
tff(365,plain,
sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[320,364]) ).
tff(366,plain,
sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[365,352,349,339,34]) ).
tff(367,plain,
sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x8),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[366]) ).
tff(368,plain,
sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(transitivity,[status(thm)],[367,338,22,19,10]) ).
tff(369,plain,
( heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(monotonicity,[status(thm)],[368]) ).
tff(370,plain,
( heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))),
inference(modus_ponens,[status(thm)],[292,370]) ).
tff(372,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x8 )
| ~ heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x8 )
| ~ heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(373,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x8 )
| ~ heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(374,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x8 )
| ~ heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(modus_ponens,[status(thm)],[373,372]) ).
tff(375,plain,
( ( x2 = x8 )
| ~ heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(unit_resolution,[status(thm)],[374,310,331]) ).
tff(376,plain,
x2 = x8,
inference(unit_resolution,[status(thm)],[375,371]) ).
tff(377,plain,
x8 = x2,
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
x13 = x2,
inference(symmetry,[status(thm)],[336]) ).
tff(379,plain,
x13 = x10,
inference(transitivity,[status(thm)],[378,319]) ).
tff(380,plain,
lseg(x13,x8) = lseg(x10,x2),
inference(monotonicity,[status(thm)],[379,377]) ).
tff(381,plain,
lseg(x10,x2) = lseg(x13,x8),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[381,32]) ).
tff(383,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(384,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[383,7]) ).
tff(385,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(386,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[385,7]) ).
tff(387,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[248]) ).
tff(388,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[388]) ).
tff(390,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[389]) ).
tff(391,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[390,386]) ).
tff(392,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[391]) ).
tff(393,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[392,384]) ).
tff(394,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[393]) ).
tff(395,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(397,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[396,7]) ).
tff(398,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(400,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[399,7]) ).
tff(401,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[400]) ).
tff(402,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[401]) ).
tff(403,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
lseg(x2,x2) = lseg(x10,x2),
inference(monotonicity,[status(thm)],[319]) ).
tff(405,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[404]) ).
tff(406,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(407,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[406,7]) ).
tff(408,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[407]) ).
tff(409,plain,
sep(lseg(x2,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[408]) ).
tff(410,plain,
^ [Sigma: $i,X: $i] :
refl(( ( sep(lseg(X,X),Sigma) = Sigma )
<=> ( sep(lseg(X,X),Sigma) = Sigma ) )),
inference(bind,[status(th)],[]) ).
tff(411,plain,
( ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
<=> ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ) ),
inference(quant_intro,[status(thm)],[410]) ).
tff(412,plain,
( ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
<=> ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ) ),
inference(rewrite,[status(thm)],[]) ).
tff(413,axiom,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV013-0.ax',normalization) ).
tff(414,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[413,412]) ).
tff(415,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(skolemize,[status(sab)],[414]) ).
tff(416,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[415,411]) ).
tff(417,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(418,plain,
sep(lseg(x2,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[417,416]) ).
tff(419,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x2),sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[418]) ).
tff(420,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[407,419,409,405,403,398,395,339]) ).
tff(421,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[420]) ).
tff(422,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(423,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[422,7]) ).
tff(424,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[25,389]) ).
tff(425,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[424]) ).
tff(426,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[425,423]) ).
tff(427,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[426]) ).
tff(428,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(430,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[429,7]) ).
tff(431,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[430]) ).
tff(432,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(monotonicity,[status(thm)],[42]) ).
tff(433,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(435,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(unit_resolution,[status(thm)],[434,7]) ).
tff(436,plain,
sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(symmetry,[status(thm)],[435]) ).
tff(437,plain,
sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(transitivity,[status(thm)],[436,433]) ).
tff(438,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(monotonicity,[status(thm)],[437]) ).
tff(439,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[438]) ).
tff(440,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[439]) ).
tff(441,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(443,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[442,7]) ).
tff(444,plain,
sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[443]) ).
tff(445,plain,
sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[444,441]) ).
tff(446,plain,
sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[445]) ).
tff(447,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[404,446]) ).
tff(448,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[446]) ).
tff(449,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[448]) ).
tff(450,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(451,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[450,416]) ).
tff(452,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[451]) ).
tff(453,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x7,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(454,plain,
sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x7,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[453,7]) ).
tff(455,plain,
sep(lseg(x7,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(457,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[456,7]) ).
tff(458,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(459,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))),
inference(unit_resolution,[status(thm)],[458,7]) ).
tff(460,plain,
sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))) = sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))),
inference(symmetry,[status(thm)],[459]) ).
tff(461,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(monotonicity,[status(thm)],[460]) ).
tff(462,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(monotonicity,[status(thm)],[461]) ).
tff(463,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(464,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(unit_resolution,[status(thm)],[463,7]) ).
tff(465,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(symmetry,[status(thm)],[464]) ).
tff(466,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(467,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))),
inference(unit_resolution,[status(thm)],[466,7]) ).
tff(468,plain,
sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))) = sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))),
inference(symmetry,[status(thm)],[49]) ).
tff(469,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) = sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))),
inference(monotonicity,[status(thm)],[468]) ).
tff(470,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))) = sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))),
inference(symmetry,[status(thm)],[469]) ).
tff(471,plain,
sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))),
inference(transitivity,[status(thm)],[460,470,467]) ).
tff(472,plain,
sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))) = sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))),
inference(monotonicity,[status(thm)],[471]) ).
tff(473,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(symmetry,[status(thm)],[472]) ).
tff(474,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(475,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))),
inference(unit_resolution,[status(thm)],[474,7]) ).
tff(476,plain,
sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))),
inference(symmetry,[status(thm)],[475]) ).
tff(477,plain,
sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(transitivity,[status(thm)],[476,473]) ).
tff(478,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(480,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))),
inference(unit_resolution,[status(thm)],[479,7]) ).
tff(481,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))),
inference(symmetry,[status(thm)],[480]) ).
tff(482,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(transitivity,[status(thm)],[481,478,465,462,432,435]) ).
tff(483,plain,
sep(lseg(x2,x13),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(monotonicity,[status(thm)],[482]) ).
tff(484,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(485,plain,
sep(lseg(x2,x13),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))),
inference(unit_resolution,[status(thm)],[484,7]) ).
tff(486,plain,
sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x2,x13),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[485]) ).
tff(487,plain,
sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(transitivity,[status(thm)],[486,483]) ).
tff(488,plain,
sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[487]) ).
tff(489,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(490,plain,
sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[489,7]) ).
tff(491,plain,
sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[491,488,457]) ).
tff(493,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x7,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[492]) ).
tff(494,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(495,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[494,7]) ).
tff(496,plain,
sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[495]) ).
tff(497,plain,
sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[496,493,455,446,452,449,447,431,428]) ).
tff(498,plain,
lseg(x13,x6) = lseg(x2,x6),
inference(monotonicity,[status(thm)],[378]) ).
tff(499,plain,
lseg(x2,x6) = lseg(x13,x6),
inference(symmetry,[status(thm)],[498]) ).
tff(500,plain,
sep(lseg(x2,x6),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[499,497]) ).
tff(501,plain,
sep(lseg(x7,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[493]) ).
tff(502,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[449]) ).
tff(503,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[447]) ).
tff(504,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(505,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[504,7]) ).
tff(506,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[424]) ).
tff(507,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),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(x2,x13),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(509,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[508,7]) ).
tff(510,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[509]) ).
tff(511,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[510,507]) ).
tff(512,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[511]) ).
tff(513,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(514,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[513,7]) ).
tff(515,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[514]) ).
tff(516,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[515,512,505,427,430,503,502,451,448,454,501,495]) ).
tff(517,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[213,210]) ).
tff(518,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[517]) ).
tff(519,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(520,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(unit_resolution,[status(thm)],[519,7]) ).
tff(521,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(symmetry,[status(thm)],[520]) ).
tff(522,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(523,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[522,7]) ).
tff(524,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[249]) ).
tff(525,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(526,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[525,7]) ).
tff(527,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[526]) ).
tff(528,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[527,524]) ).
tff(529,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[528]) ).
tff(530,plain,
sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[530]) ).
tff(532,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[531,523]) ).
tff(533,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[532]) ).
tff(534,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(536,plain,
sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[535,7]) ).
tff(537,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[536]) ).
tff(538,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(539,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[538,7]) ).
tff(540,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(541,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(unit_resolution,[status(thm)],[540,7]) ).
tff(542,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[541]) ).
tff(543,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(transitivity,[status(thm)],[542,265]) ).
tff(544,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[543]) ).
tff(545,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[544]) ).
tff(546,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[527,524,545,539]) ).
tff(547,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[546]) ).
tff(548,plain,
sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),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(x14,x12),sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(550,plain,
sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[549,7]) ).
tff(551,plain,
sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[550]) ).
tff(552,plain,
sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[551,548]) ).
tff(553,plain,
sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[552]) ).
tff(554,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[404,553]) ).
tff(555,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[553]) ).
tff(556,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[555]) ).
tff(557,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(558,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[557,416]) ).
tff(559,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[558]) ).
tff(560,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(561,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[560,7]) ).
tff(562,plain,
sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[527]) ).
tff(563,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[562]) ).
tff(564,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[563]) ).
tff(565,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(566,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(unit_resolution,[status(thm)],[565,7]) ).
tff(567,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[566]) ).
tff(568,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(transitivity,[status(thm)],[567,438,387]) ).
tff(569,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),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(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(571,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[570,7]) ).
tff(572,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[571]) ).
tff(573,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[572,569,249]) ).
tff(574,plain,
sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(576,plain,
sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[575,7]) ).
tff(577,plain,
sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[576]) ).
tff(578,plain,
sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[577,574]) ).
tff(579,plain,
sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[578]) ).
tff(580,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(581,plain,
sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[580,7]) ).
tff(582,plain,
sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[581]) ).
tff(583,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))),
inference(symmetry,[status(thm)],[50]) ).
tff(584,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(585,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))),
inference(unit_resolution,[status(thm)],[584,7]) ).
tff(586,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) = sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))),
inference(symmetry,[status(thm)],[585]) ).
tff(587,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))),
inference(transitivity,[status(thm)],[586,583]) ).
tff(588,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(monotonicity,[status(thm)],[587]) ).
tff(589,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(590,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))),
inference(unit_resolution,[status(thm)],[589,7]) ).
tff(591,plain,
sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))),
inference(symmetry,[status(thm)],[590]) ).
tff(592,plain,
sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(transitivity,[status(thm)],[591,588]) ).
tff(593,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(monotonicity,[status(thm)],[592]) ).
tff(594,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(595,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))),
inference(unit_resolution,[status(thm)],[594,7]) ).
tff(596,plain,
sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))),
inference(symmetry,[status(thm)],[595]) ).
tff(597,plain,
sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(transitivity,[status(thm)],[596,593]) ).
tff(598,plain,
sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(monotonicity,[status(thm)],[597]) ).
tff(599,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(600,plain,
sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))),
inference(unit_resolution,[status(thm)],[599,7]) ).
tff(601,plain,
sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[600]) ).
tff(602,plain,
sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(transitivity,[status(thm)],[601,598]) ).
tff(603,plain,
sep(lseg(x2,x13),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[602]) ).
tff(604,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(605,plain,
sep(lseg(x2,x13),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[604,7]) ).
tff(606,plain,
sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))),
inference(symmetry,[status(thm)],[605]) ).
tff(607,plain,
sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[606,603]) ).
tff(608,plain,
sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[607]) ).
tff(609,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(610,plain,
sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[609,7]) ).
tff(611,plain,
sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[610]) ).
tff(612,plain,
sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[611,608]) ).
tff(613,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[612]) ).
tff(614,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(615,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[614,7]) ).
tff(616,plain,
sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[615]) ).
tff(617,plain,
sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(transitivity,[status(thm)],[616,613,582,579,564,561,559,556,554,537,534]) ).
tff(618,plain,
sep(lseg(x2,x6),sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(monotonicity,[status(thm)],[499,617]) ).
tff(619,plain,
sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[613]) ).
tff(620,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[579]) ).
tff(621,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[564]) ).
tff(622,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[561]) ).
tff(623,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[556]) ).
tff(624,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[554]) ).
tff(625,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[223]) ).
tff(626,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(627,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(unit_resolution,[status(thm)],[626,7]) ).
tff(628,plain,
sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(symmetry,[status(thm)],[627]) ).
tff(629,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[189]) ).
tff(630,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(631,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(unit_resolution,[status(thm)],[630,7]) ).
tff(632,plain,
sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[631]) ).
tff(633,plain,
sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[632,629]) ).
tff(634,plain,
sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[320,633]) ).
tff(635,plain,
sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[634,628,625,533,536,624,623,558,622,621,620,581,619,615]) ).
tff(636,plain,
sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x2,x6),sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[635]) ).
tff(637,plain,
sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(transitivity,[status(thm)],[636,618,521,518,10]) ).
tff(638,plain,
( heap(sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(monotonicity,[status(thm)],[637]) ).
tff(639,plain,
( heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(symmetry,[status(thm)],[638]) ).
tff(640,plain,
heap(sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))),
inference(modus_ponens,[status(thm)],[292,639]) ).
tff(641,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x6 )
| ~ heap(sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x6 )
| ~ heap(sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(642,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x6 )
| ~ heap(sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(643,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x6 )
| ~ heap(sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(modus_ponens,[status(thm)],[642,641]) ).
tff(644,plain,
( ( x2 = x6 )
| ~ heap(sep(lseg(x2,x6),sep(lseg(x2,x3),sep(lseg(x13,x8),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(unit_resolution,[status(thm)],[643,310,331]) ).
tff(645,plain,
x2 = x6,
inference(unit_resolution,[status(thm)],[644,640]) ).
tff(646,plain,
x6 = x2,
inference(symmetry,[status(thm)],[645]) ).
tff(647,plain,
lseg(x2,x6) = lseg(x10,x2),
inference(monotonicity,[status(thm)],[319,646]) ).
tff(648,plain,
lseg(x10,x2) = lseg(x2,x6),
inference(symmetry,[status(thm)],[647]) ).
tff(649,plain,
sep(lseg(x10,x2),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))) = sep(lseg(x2,x6),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[648,516]) ).
tff(650,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[512]) ).
tff(651,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(symmetry,[status(thm)],[505]) ).
tff(652,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(transitivity,[status(thm)],[452,449,447,431,428,651,650,514]) ).
tff(653,plain,
sep(lseg(x10,x2),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x10,x2),sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))),
inference(monotonicity,[status(thm)],[652]) ).
tff(654,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[106]) ).
tff(655,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[182]) ).
tff(656,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(transitivity,[status(thm)],[655,654]) ).
tff(657,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[656]) ).
tff(658,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(659,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(unit_resolution,[status(thm)],[658,7]) ).
tff(660,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[659]) ).
tff(661,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[660,657]) ).
tff(662,plain,
lseg(x2,x13) = lseg(x10,x2),
inference(monotonicity,[status(thm)],[319,378]) ).
tff(663,plain,
lseg(x10,x2) = lseg(x2,x13),
inference(symmetry,[status(thm)],[662]) ).
tff(664,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))) = sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[663,661]) ).
tff(665,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[657]) ).
tff(666,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[425]) ).
tff(667,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[423]) ).
tff(668,plain,
sep(lseg(x2,x2),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(monotonicity,[status(thm)],[404,445]) ).
tff(669,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(670,plain,
sep(lseg(x2,x2),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(unit_resolution,[status(thm)],[669,416]) ).
tff(671,plain,
sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x2,x2),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(symmetry,[status(thm)],[670]) ).
tff(672,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))),
inference(transitivity,[status(thm)],[440,443,671,668,667,666,665,659]) ).
tff(673,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))),
inference(monotonicity,[status(thm)],[672]) ).
tff(674,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x6,x14),sep(lseg(x6,x16),emp)) = sep(lseg(x6,x16),sep(lseg(x6,x14),emp)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(675,plain,
sep(lseg(x6,x14),sep(lseg(x6,x16),emp)) = sep(lseg(x6,x16),sep(lseg(x6,x14),emp)),
inference(unit_resolution,[status(thm)],[674,7]) ).
tff(676,plain,
sep(lseg(x6,x16),sep(lseg(x6,x14),emp)) = sep(lseg(x6,x14),sep(lseg(x6,x16),emp)),
inference(symmetry,[status(thm)],[675]) ).
tff(677,plain,
sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))),
inference(monotonicity,[status(thm)],[676]) ).
tff(678,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))),
inference(monotonicity,[status(thm)],[677]) ).
tff(679,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(680,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))),
inference(unit_resolution,[status(thm)],[679,7]) ).
tff(681,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[680]) ).
tff(682,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))),
inference(transitivity,[status(thm)],[681,678]) ).
tff(683,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(monotonicity,[status(thm)],[682]) ).
tff(684,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(685,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[684,7]) ).
tff(686,plain,
sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[685]) ).
tff(687,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(688,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))),
inference(unit_resolution,[status(thm)],[687,7]) ).
tff(689,plain,
sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))),
inference(monotonicity,[status(thm)],[676]) ).
tff(690,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))) = sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[689]) ).
tff(691,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[690]) ).
tff(692,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(693,plain,
sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))),
inference(unit_resolution,[status(thm)],[692,7]) ).
tff(694,plain,
sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[693]) ).
tff(695,plain,
sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))),
inference(transitivity,[status(thm)],[694,689]) ).
tff(696,plain,
sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))),
inference(monotonicity,[status(thm)],[695]) ).
tff(697,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(698,plain,
sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(unit_resolution,[status(thm)],[697,7]) ).
tff(699,plain,
sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[698]) ).
tff(700,plain,
sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[699,696,691,688]) ).
tff(701,plain,
sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[700]) ).
tff(702,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(703,plain,
sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[702,7]) ).
tff(704,plain,
sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[703]) ).
tff(705,plain,
sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))),
inference(transitivity,[status(thm)],[704,701,686,683,43]) ).
tff(706,plain,
sep(lseg(x7,x2),sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(monotonicity,[status(thm)],[705]) ).
tff(707,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(708,plain,
sep(lseg(x7,x2),sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[707,7]) ).
tff(709,plain,
sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[708]) ).
tff(710,plain,
sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(transitivity,[status(thm)],[709,706]) ).
tff(711,plain,
sep(lseg(x10,x3),sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(monotonicity,[status(thm)],[710]) ).
tff(712,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(713,plain,
sep(lseg(x10,x3),sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[712,7]) ).
tff(714,plain,
sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x3),sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[713]) ).
tff(715,plain,
sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(transitivity,[status(thm)],[714,711,248]) ).
tff(716,plain,
sep(lseg(x14,x12),sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))),
inference(monotonicity,[status(thm)],[715]) ).
tff(717,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x6,x16),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(718,plain,
sep(lseg(x14,x12),sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x6,x16),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(unit_resolution,[status(thm)],[717,7]) ).
tff(719,plain,
sep(lseg(x6,x16),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(symmetry,[status(thm)],[718]) ).
tff(720,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(721,plain,
sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[720,416]) ).
tff(722,plain,
lseg(x10,x2) = lseg(x2,x2),
inference(symmetry,[status(thm)],[404]) ).
tff(723,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[722]) ).
tff(724,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[380]) ).
tff(725,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(726,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))),
inference(unit_resolution,[status(thm)],[725,7]) ).
tff(727,plain,
sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[726]) ).
tff(728,plain,
sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[727]) ).
tff(729,plain,
sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[728]) ).
tff(730,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(731,plain,
sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[730,7]) ).
tff(732,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[727]) ).
tff(733,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[732]) ).
tff(734,plain,
sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[733]) ).
tff(735,plain,
sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[734,731,729]) ).
tff(736,plain,
sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),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(x11,x4),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(738,plain,
sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[737,7]) ).
tff(739,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(740,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))),
inference(unit_resolution,[status(thm)],[739,7]) ).
tff(741,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[740]) ).
tff(742,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[741]) ).
tff(743,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[742]) ).
tff(744,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x14),sep(lseg(x6,x14),emp)) = sep(lseg(x6,x14),sep(lseg(x3,x14),emp)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(745,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),emp)) = sep(lseg(x6,x14),sep(lseg(x3,x14),emp)),
inference(unit_resolution,[status(thm)],[744,7]) ).
tff(746,plain,
sep(lseg(x6,x14),sep(lseg(x3,x14),emp)) = sep(lseg(x3,x14),sep(lseg(x6,x14),emp)),
inference(symmetry,[status(thm)],[745]) ).
tff(747,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))),
inference(monotonicity,[status(thm)],[746]) ).
tff(748,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))),
inference(symmetry,[status(thm)],[747]) ).
tff(749,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(monotonicity,[status(thm)],[748]) ).
tff(750,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[749]) ).
tff(751,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(752,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(unit_resolution,[status(thm)],[751,7]) ).
tff(753,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[752]) ).
tff(754,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))),
inference(monotonicity,[status(thm)],[746]) ).
tff(755,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[754]) ).
tff(756,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[755]) ).
tff(757,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[756,753,750,743]) ).
tff(758,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[757]) ).
tff(759,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[758]) ).
tff(760,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(761,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[760,7]) ).
tff(762,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[741]) ).
tff(763,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[762]) ).
tff(764,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[763]) ).
tff(765,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[764,761,759]) ).
tff(766,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[765]) ).
tff(767,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[764]) ).
tff(768,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[761]) ).
tff(769,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[768,767]) ).
tff(770,plain,
sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[769]) ).
tff(771,plain,
sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[770,766,738,736]) ).
tff(772,plain,
sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[771]) ).
tff(773,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(774,plain,
sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[773,7]) ).
tff(775,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[769]) ).
tff(776,plain,
sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[775]) ).
tff(777,plain,
sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[776]) ).
tff(778,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(779,plain,
sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[778,416]) ).
tff(780,plain,
sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[404]) ).
tff(781,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[780]) ).
tff(782,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[775]) ).
tff(783,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(784,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[783,7]) ).
tff(785,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[784]) ).
tff(786,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[769]) ).
tff(787,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[786]) ).
tff(788,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(monotonicity,[status(thm)],[748]) ).
tff(789,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[788]) ).
tff(790,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(791,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(unit_resolution,[status(thm)],[790,7]) ).
tff(792,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[791]) ).
tff(793,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[792,789]) ).
tff(794,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[793]) ).
tff(795,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[794]) ).
tff(796,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(797,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[796,7]) ).
tff(798,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[793]) ).
tff(799,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(symmetry,[status(thm)],[798]) ).
tff(800,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(monotonicity,[status(thm)],[799]) ).
tff(801,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[762]) ).
tff(802,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(803,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[802,7]) ).
tff(804,plain,
sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[741]) ).
tff(805,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[804]) ).
tff(806,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[805]) ).
tff(807,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[747]) ).
tff(808,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(809,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(unit_resolution,[status(thm)],[808,7]) ).
tff(810,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[809]) ).
tff(811,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[810,807]) ).
tff(812,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[811]) ).
tff(813,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(814,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(unit_resolution,[status(thm)],[813,7]) ).
tff(815,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(symmetry,[status(thm)],[814]) ).
tff(816,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[815,812,806,803,801]) ).
tff(817,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[816]) ).
tff(818,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(819,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[818,7]) ).
tff(820,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(symmetry,[status(thm)],[819]) ).
tff(821,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(822,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(unit_resolution,[status(thm)],[821,7]) ).
tff(823,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[754]) ).
tff(824,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(825,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(unit_resolution,[status(thm)],[824,7]) ).
tff(826,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[825]) ).
tff(827,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[826,823]) ).
tff(828,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[827]) ).
tff(829,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(symmetry,[status(thm)],[828]) ).
tff(830,plain,
sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[727]) ).
tff(831,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[830]) ).
tff(832,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[831]) ).
tff(833,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[832]) ).
tff(834,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(835,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[834,7]) ).
tff(836,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[835]) ).
tff(837,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[727]) ).
tff(838,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[837]) ).
tff(839,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[838]) ).
tff(840,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(transitivity,[status(thm)],[839,836,833,829,822]) ).
tff(841,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(monotonicity,[status(thm)],[840]) ).
tff(842,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[841,820,817,800,797,795,787]) ).
tff(843,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[842]) ).
tff(844,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[843,785,782,781,779]) ).
tff(845,plain,
sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[844]) ).
tff(846,plain,
sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(transitivity,[status(thm)],[845,777,774,772]) ).
tff(847,plain,
sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[846]) ).
tff(848,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(849,plain,
sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))),
inference(unit_resolution,[status(thm)],[848,7]) ).
tff(850,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[844]) ).
tff(851,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(symmetry,[status(thm)],[850]) ).
tff(852,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(853,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[852,7]) ).
tff(854,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[732]) ).
tff(855,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(856,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[855,7]) ).
tff(857,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[856]) ).
tff(858,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[837]) ).
tff(859,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[858]) ).
tff(860,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))),
inference(symmetry,[status(thm)],[754]) ).
tff(861,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(monotonicity,[status(thm)],[860]) ).
tff(862,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[861]) ).
tff(863,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(864,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(unit_resolution,[status(thm)],[863,7]) ).
tff(865,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[864]) ).
tff(866,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[865,862]) ).
tff(867,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[866]) ).
tff(868,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[867,859,857,854,758,768,767]) ).
tff(869,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[868]) ).
tff(870,plain,
sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(symmetry,[status(thm)],[869]) ).
tff(871,plain,
sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(transitivity,[status(thm)],[870,853]) ).
tff(872,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))))),
inference(monotonicity,[status(thm)],[871]) ).
tff(873,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[872]) ).
tff(874,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(875,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))))),
inference(unit_resolution,[status(thm)],[874,7]) ).
tff(876,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[866]) ).
tff(877,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(symmetry,[status(thm)],[876]) ).
tff(878,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(monotonicity,[status(thm)],[877]) ).
tff(879,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[878]) ).
tff(880,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(881,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[880,7]) ).
tff(882,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(symmetry,[status(thm)],[881]) ).
tff(883,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[882,879]) ).
tff(884,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[883]) ).
tff(885,plain,
sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))))),
inference(symmetry,[status(thm)],[884]) ).
tff(886,plain,
sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(transitivity,[status(thm)],[885,875,873,851]) ).
tff(887,plain,
sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))),
inference(monotonicity,[status(thm)],[886]) ).
tff(888,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[858]) ).
tff(889,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[888]) ).
tff(890,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(891,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[890,7]) ).
tff(892,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[891]) ).
tff(893,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[892,889]) ).
tff(894,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[893]) ).
tff(895,plain,
sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[894]) ).
tff(896,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(897,plain,
sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[896,7]) ).
tff(898,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[897]) ).
tff(899,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[893]) ).
tff(900,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[899]) ).
tff(901,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(monotonicity,[status(thm)],[877]) ).
tff(902,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[901]) ).
tff(903,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(904,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[903,7]) ).
tff(905,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[868]) ).
tff(906,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(symmetry,[status(thm)],[905]) ).
tff(907,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[906,904,902,900]) ).
tff(908,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[907]) ).
tff(909,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[758,768,767]) ).
tff(910,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[909]) ).
tff(911,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(912,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[911,7]) ).
tff(913,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[912]) ).
tff(914,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[913,910]) ).
tff(915,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[914]) ).
tff(916,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(917,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[916,7]) ).
tff(918,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(919,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[918,7]) ).
tff(920,plain,
sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[919]) ).
tff(921,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(922,plain,
sep(lseg(x2,x2),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[921,416]) ).
tff(923,plain,
sep(lseg(x2,x2),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[404,920]) ).
tff(924,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x2,x2),sep(lseg(x13,x8),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[923]) ).
tff(925,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(926,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[925,7]) ).
tff(927,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[926]) ).
tff(928,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(929,plain,
sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[928,7]) ).
tff(930,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[732]) ).
tff(931,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(932,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[931,7]) ).
tff(933,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[831]) ).
tff(934,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[933,932,930]) ).
tff(935,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[934]) ).
tff(936,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[935,929]) ).
tff(937,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[936]) ).
tff(938,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[937,927,924,922,920]) ).
tff(939,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[938]) ).
tff(940,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(transitivity,[status(thm)],[939,917,915,908,898,895]) ).
tff(941,plain,
sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) = sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[940]) ).
tff(942,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(943,plain,
sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))),
inference(unit_resolution,[status(thm)],[942,7]) ).
tff(944,plain,
sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) = sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))),
inference(symmetry,[status(thm)],[943]) ).
tff(945,plain,
sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[938]) ).
tff(946,plain,
sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(symmetry,[status(thm)],[945]) ).
tff(947,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(948,plain,
sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[947,7]) ).
tff(949,plain,
sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[948]) ).
tff(950,plain,
sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[735]) ).
tff(951,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(952,plain,
sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[951,7]) ).
tff(953,plain,
sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[952,950]) ).
tff(954,plain,
sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[953]) ).
tff(955,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[954]) ).
tff(956,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(transitivity,[status(thm)],[955,949,946]) ).
tff(957,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))),
inference(monotonicity,[status(thm)],[956]) ).
tff(958,plain,
sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[320]) ).
tff(959,plain,
sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(transitivity,[status(thm)],[958,957,944,941,887,849,847,724,723,721]) ).
tff(960,plain,
lseg(x2,x16) = lseg(x6,x16),
inference(monotonicity,[status(thm)],[645]) ).
tff(961,plain,
sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) = sep(lseg(x6,x16),sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[960,959]) ).
tff(962,plain,
sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(transitivity,[status(thm)],[961,719,716,440,443,671,668,673,664,427,430,653,649,500,35,32,394,397,402,421,382,22,19,10]) ).
tff(963,plain,
( heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))))))
<=> heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))))))) ),
inference(monotonicity,[status(thm)],[962]) ).
tff(964,plain,
( heap(sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))))
<=> heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ),
inference(symmetry,[status(thm)],[963]) ).
tff(965,plain,
heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))),
inference(modus_ponens,[status(thm)],[292,964]) ).
tff(966,plain,
( ( x2 != x16 )
<=> ( x2 != x16 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(967,axiom,
x2 != x16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_8) ).
tff(968,plain,
x2 != x16,
inference(modus_ponens,[status(thm)],[967,966]) ).
tff(969,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x16 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x16 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(970,plain,
( ( ( x2 = x3 )
| ( x2 = x16 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) )
<=> ( ( x2 = x16 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(971,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x16 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x16 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ) ),
inference(monotonicity,[status(thm)],[970]) ).
tff(972,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x16 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x16 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ) ),
inference(transitivity,[status(thm)],[971,969]) ).
tff(973,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x3 )
| ( x2 = x16 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(974,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x16 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ),
inference(modus_ponens,[status(thm)],[973,972]) ).
tff(975,plain,
~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))),
inference(unit_resolution,[status(thm)],[974,310,968,331]) ).
tff(976,plain,
$false,
inference(unit_resolution,[status(thm)],[975,965]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW438-1 : TPTP v9.0.0. Released v5.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Jun 20 11:41:55 EDT 2025
% 0.15/0.36 % CPUTime :
% 11.14/11.32 % SZS status Unsatisfiable
% 11.14/11.32 % SZS output start Proof
% See solution above
% 11.44/11.63 % E exiting
%------------------------------------------------------------------------------