TSTP Solution File: SWW438-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW438-1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:58:40 EDT 2022
% Result : Unsatisfiable 6.56s 4.45s
% Output : Proof 6.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 200
% Syntax : Number of formulae : 991 ( 763 unt; 16 typ; 0 def)
% Number of atoms : 1359 (1245 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 657 ( 277 ~; 338 |; 0 &)
% ( 42 <=>; 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 : 5 ( 3 >; 2 *; 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 : 667 ( 654 !; 0 ?; 667 :)
% 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(x8_type,type,
x8: $i ).
tff(x13_type,type,
x13: $i ).
tff(x2_type,type,
x2: $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(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(24,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)],[23,7]) ).
tff(25,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(26,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)],[25,7]) ).
tff(27,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(28,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)],[27,7]) ).
tff(29,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)],[28]) ).
tff(30,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)],[29]) ).
tff(31,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)],[30]) ).
tff(32,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)],[31]) ).
tff(33,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)],[32,26]) ).
tff(34,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)],[33]) ).
tff(35,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)],[34,24]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36]) ).
tff(38,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(39,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)],[38,7]) ).
tff(40,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)],[39]) ).
tff(41,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(42,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)],[41,7]) ).
tff(43,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)],[42]) ).
tff(44,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)],[43]) ).
tff(45,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)],[44]) ).
tff(46,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(47,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)],[46,7]) ).
tff(48,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)],[47]) ).
tff(49,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(50,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)],[49,7]) ).
tff(51,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(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)],[50]) ).
tff(52,plain,
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(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)],[51]) ).
tff(53,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(symmetry,[status(thm)],[52]) ).
tff(54,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)],[53]) ).
tff(55,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)],[54]) ).
tff(56,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(57,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)],[56,7]) ).
tff(58,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)],[57]) ).
tff(59,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)],[58,55]) ).
tff(60,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)],[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(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(62,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)],[61,7]) ).
tff(63,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)],[62]) ).
tff(64,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,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(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(65,plain,
sep(lseg(x14,x12),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(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)],[64,7]) ).
tff(66,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)],[50]) ).
tff(67,plain,
sep(lseg(x14,x12),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(x14,x12),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)],[66]) ).
tff(68,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)],[66]) ).
tff(69,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(70,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)],[69,7]) ).
tff(71,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)],[70]) ).
tff(72,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(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)],[71,68]) ).
tff(73,plain,
sep(lseg(x14,x12),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(x14,x12),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)],[72]) ).
tff(74,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(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(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(75,plain,
sep(lseg(x14,x12),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(x14,x12),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)],[74,7]) ).
tff(76,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),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(x14,x12),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)],[75]) ).
tff(77,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),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(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)],[76,73,67,65]) ).
tff(78,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x14,x12),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(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)],[77]) ).
tff(79,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(x14,x12),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(x13,x6),sep(lseg(x14,x12),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(80,plain,
sep(lseg(x13,x6),sep(lseg(x10,x2),sep(lseg(x14,x12),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(x13,x6),sep(lseg(x14,x12),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)],[79,7]) ).
tff(81,plain,
sep(lseg(x10,x2),sep(lseg(x13,x6),sep(lseg(x14,x12),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(x13,x6),sep(lseg(x10,x2),sep(lseg(x14,x12),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)],[80]) ).
tff(82,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)],[28]) ).
tff(83,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)],[82]) ).
tff(84,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(85,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)],[84,7]) ).
tff(86,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)],[85]) ).
tff(87,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)],[86,83]) ).
tff(88,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(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)],[87]) ).
tff(89,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(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)],[88]) ).
tff(90,plain,
sep(lseg(x14,x12),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(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)],[89]) ).
tff(91,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(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)],[90]) ).
tff(92,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(93,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)],[92,7]) ).
tff(94,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)],[93]) ).
tff(95,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(96,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)],[95,7]) ).
tff(97,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(98,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)],[97,7]) ).
tff(99,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)],[98]) ).
tff(100,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)],[99]) ).
tff(101,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(102,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)],[101,7]) ).
tff(103,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)],[102]) ).
tff(104,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)],[103,100]) ).
tff(105,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)],[104]) ).
tff(106,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)],[105]) ).
tff(107,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)],[86,83,106,96]) ).
tff(108,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)],[107]) ).
tff(109,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)],[108]) ).
tff(110,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(111,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)],[110,7]) ).
tff(112,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)],[111]) ).
tff(113,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)],[112,109]) ).
tff(114,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)],[113]) ).
tff(115,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(x14,x12),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(transitivity,[status(thm)],[114,94,91]) ).
tff(116,plain,
sep(lseg(x13,x6),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(x13,x6),sep(lseg(x14,x12),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(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),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(x13,x6),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(118,plain,
sep(lseg(x13,x6),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(x13,x6),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)],[117,7]) ).
tff(119,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),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(x13,x6),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)],[118]) ).
tff(120,plain,
sep(lseg(x13,x6),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(x13,x6),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)],[113]) ).
tff(121,plain,
sep(lseg(x13,x6),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(x13,x6),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)],[120]) ).
tff(122,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(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,x6),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(123,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),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,x6),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)],[122,7]) ).
tff(124,plain,
sep(lseg(x13,x6),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,x6),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)],[87]) ).
tff(125,plain,
sep(lseg(x13,x6),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(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)],[124]) ).
tff(126,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),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(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)],[125]) ).
tff(127,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),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(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(transitivity,[status(thm)],[126,123,121]) ).
tff(128,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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(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)],[127]) ).
tff(129,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)],[100]) ).
tff(130,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(131,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)],[130,7]) ).
tff(132,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)],[131]) ).
tff(133,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,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)],[132,129]) ).
tff(134,plain,
sep(lseg(x13,x6),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,x6),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)],[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(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(x13,x6),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(136,plain,
sep(lseg(x13,x6),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(x13,x6),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)],[135,7]) ).
tff(137,plain,
sep(lseg(x10,x3),sep(lseg(x13,x6),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(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)],[136]) ).
tff(138,plain,
sep(lseg(x10,x3),sep(lseg(x13,x6),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,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)],[137,134]) ).
tff(139,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x6),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(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)],[138]) ).
tff(140,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(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(x13,x6),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(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x6),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(x13,x6),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(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),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(x13,x6),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(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),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(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)],[142,139]) ).
tff(144,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),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,x6),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)],[143]) ).
tff(145,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(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(x14,x12),sep(lseg(x13,x6),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(146,plain,
sep(lseg(x2,x13),sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x6),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(x14,x12),sep(lseg(x13,x6),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)],[145,7]) ).
tff(147,plain,
sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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(x14,x12),sep(lseg(x13,x6),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)],[146]) ).
tff(148,plain,
sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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(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)],[147,144,128,119,116]) ).
tff(149,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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(x14,x12),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(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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)],[149,81,78,63,60,10]) ).
tff(151,plain,
( heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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)],[150]) ).
tff(152,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(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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)],[151]) ).
tff(153,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(154,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(155,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)],[154,153]) ).
tff(156,plain,
heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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)],[155,152]) ).
tff(157,plain,
( ( x10 = x3 )
<=> ( x3 = x10 ) ),
inference(commutativity,[status(thm)],]) ).
tff(158,plain,
( ( x3 = x10 )
<=> ( x10 = x3 ) ),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
( ( x3 != x10 )
<=> ( x10 != x3 ) ),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
( ( x3 != x10 )
<=> ( x3 != x10 ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,axiom,
x3 != x10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).
tff(162,plain,
x3 != x10,
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
x10 != x3,
inference(modus_ponens,[status(thm)],[162,159]) ).
tff(164,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(165,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)],[164]) ).
tff(166,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(167,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(168,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)],[167]) ).
tff(169,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(170,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)],[169,168]) ).
tff(171,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)],[170,166]) ).
tff(172,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)],[171]) ).
tff(173,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)],[172,165]) ).
tff(174,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(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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 = x3 )
| ( x10 = x2 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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(175,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(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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(176,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(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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)],[175,174]) ).
tff(177,plain,
( ( x10 = x2 )
| ~ heap(sep(lseg(x10,x2),sep(lseg(x10,x3),sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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)],[176,173,163]) ).
tff(178,plain,
x10 = x2,
inference(unit_resolution,[status(thm)],[177,156]) ).
tff(179,plain,
x2 = x10,
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
lseg(x2,x2) = lseg(x10,x2),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,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(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)],[180,48]) ).
tff(182,plain,
^ [Sigma: $i,X: $i] :
refl(
( ( sep(lseg(X,X),Sigma) = Sigma )
<=> ( sep(lseg(X,X),Sigma) = Sigma ) )),
inference(bind,[status(th)],]) ).
tff(183,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)],[182]) ).
tff(184,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(185,axiom,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV013-0.ax',normalization) ).
tff(186,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(skolemize,[status(sab)],[186]) ).
tff(188,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[187,183]) ).
tff(189,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(190,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)],[189,188]) ).
tff(191,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)],[190]) ).
tff(192,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(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)],[47,191,181,45,40,37]) ).
tff(193,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(194,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)],[193,7]) ).
tff(195,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)],[194]) ).
tff(196,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)],[195]) ).
tff(197,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(198,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)],[197,7]) ).
tff(199,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)],[198]) ).
tff(200,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)],[199,196]) ).
tff(201,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)],[200]) ).
tff(202,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(203,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)],[202,7]) ).
tff(204,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)],[203]) ).
tff(205,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)],[204,201]) ).
tff(206,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)],[205]) ).
tff(207,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(208,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)],[207,7]) ).
tff(209,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)],[208]) ).
tff(210,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,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(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(211,plain,
sep(lseg(x13,x6),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,x6),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)],[210,7]) ).
tff(212,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)],[99]) ).
tff(213,plain,
sep(lseg(x13,x6),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,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)],[212]) ).
tff(214,plain,
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(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)],[213]) ).
tff(215,plain,
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,x2),sep(lseg(x13,x6),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)],[214,211]) ).
tff(216,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(x10,x2),sep(lseg(x13,x6),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)],[215]) ).
tff(217,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),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(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(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),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,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)],[217]) ).
tff(219,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,x6),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,x6),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(220,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x13,x6),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,x6),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)],[219,7]) ).
tff(221,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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(x10,x2),sep(lseg(x13,x6),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)],[220]) ).
tff(222,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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,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)],[221,218]) ).
tff(223,plain,
lseg(x2,x3) = lseg(x10,x3),
inference(monotonicity,[status(thm)],[179]) ).
tff(224,plain,
sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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(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)],[223,222]) ).
tff(225,plain,
sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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,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)],[224,209,206]) ).
tff(226,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),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(x13,x6),sep(lseg(x14,x12),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(transitivity,[status(thm)],[119,116]) ).
tff(227,plain,
sep(lseg(x2,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),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(x13,x6),sep(lseg(x14,x12),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(monotonicity,[status(thm)],[180,226]) ).
tff(228,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),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(x13,x6),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)],[116]) ).
tff(229,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)],[82]) ).
tff(230,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(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)],[229]) ).
tff(231,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(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(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(232,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(x13,x8),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)],[231,7]) ).
tff(233,plain,
sep(lseg(x13,x8),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(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)],[232]) ).
tff(234,plain,
sep(lseg(x13,x8),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(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)],[233,230]) ).
tff(235,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),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(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)],[234]) ).
tff(236,plain,
sep(lseg(x14,x12),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(x14,x12),sep(lseg(x13,x8),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)],[235]) ).
tff(237,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),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(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),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)],[236]) ).
tff(238,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),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(x13,x6),sep(lseg(x14,x12),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)],[237]) ).
tff(239,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(x13,x8),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(x13,x6),sep(lseg(x13,x8),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(240,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),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(x13,x6),sep(lseg(x13,x8),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)],[239,7]) ).
tff(241,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),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(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),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)],[240]) ).
tff(242,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),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(x13,x6),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(transitivity,[status(thm)],[241,238,228,118]) ).
tff(243,plain,
sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),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,x2),sep(lseg(x2,x13),sep(lseg(x13,x6),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)],[242]) ).
tff(244,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),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(x13,x6),sep(lseg(x13,x8),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(245,plain,
sep(lseg(x2,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),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(x13,x6),sep(lseg(x13,x8),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)],[244,188]) ).
tff(246,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),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,x2),sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),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)],[245]) ).
tff(247,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(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)],[133]) ).
tff(248,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(249,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)],[248,7]) ).
tff(250,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)],[249]) ).
tff(251,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(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)],[250,247]) ).
tff(252,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(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)],[251]) ).
tff(253,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(254,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)],[253,7]) ).
tff(255,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)],[254]) ).
tff(256,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(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)],[255,252]) ).
tff(257,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(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)],[256]) ).
tff(258,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(259,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)],[258,7]) ).
tff(260,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)],[259]) ).
tff(261,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(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(x2,x13),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(262,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(x13,x8),sep(lseg(x2,x13),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)],[261,7]) ).
tff(263,plain,
sep(lseg(x13,x8),sep(lseg(x2,x13),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,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)],[262]) ).
tff(264,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x2,x13),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,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)],[263]) ).
tff(265,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(x13,x8),sep(lseg(x2,x13),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)],[264]) ).
tff(266,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(x14,x12),sep(lseg(x13,x8),sep(lseg(x2,x13),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)],[265]) ).
tff(267,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x2,x13),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,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)],[266]) ).
tff(268,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(x13,x8),sep(lseg(x2,x13),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(x13,x8),sep(lseg(x2,x13),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(269,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x2,x13),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(x13,x8),sep(lseg(x2,x13),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)],[268,7]) ).
tff(270,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x2,x13),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(x2,x13),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)],[269]) ).
tff(271,plain,
sep(lseg(x13,x6),sep(lseg(x13,x8),sep(lseg(x2,x13),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(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)],[263]) ).
tff(272,plain,
sep(lseg(x13,x6),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(x13,x8),sep(lseg(x2,x13),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)],[271]) ).
tff(273,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),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(x13,x8),sep(lseg(x2,x13),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)],[272]) ).
tff(274,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(275,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)],[274,7]) ).
tff(276,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(277,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)],[276,7]) ).
tff(278,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)],[277]) ).
tff(279,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)],[278]) ).
tff(280,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)],[279]) ).
tff(281,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(x3,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))),
inference(transitivity,[status(thm)],[99,280,275]) ).
tff(282,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(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)],[281]) ).
tff(283,plain,
sep(lseg(x13,x8),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(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)],[282]) ).
tff(284,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(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(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(285,plain,
sep(lseg(x13,x8),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(x3,x14),sep(lseg(x13,x8),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)],[284,7]) ).
tff(286,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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)],[286,283]) ).
tff(288,plain,
sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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)],[287]) ).
tff(289,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(x3,x14),sep(lseg(x13,x8),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)],[288]) ).
tff(290,plain,
sep(lseg(x13,x6),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(x3,x14),sep(lseg(x13,x8),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)],[289]) ).
tff(291,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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(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)],[290]) ).
tff(292,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),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(293,plain,
sep(lseg(x13,x6),sep(lseg(x2,x13),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),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)],[292,7]) ).
tff(294,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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(x3,x14),sep(lseg(x13,x8),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)],[293]) ).
tff(295,plain,
sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))) = sep(lseg(x13,x6),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)],[287]) ).
tff(296,plain,
sep(lseg(x13,x6),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(x3,x14),sep(lseg(x13,x8),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)],[295]) ).
tff(297,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),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(x3,x14),sep(lseg(x13,x8),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)],[296]) ).
tff(298,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(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(x13,x6),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(299,plain,
sep(lseg(x13,x6),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(x13,x6),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)],[298,7]) ).
tff(300,plain,
sep(lseg(x13,x8),sep(lseg(x13,x6),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(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)],[299]) ).
tff(301,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),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(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)],[300]) ).
tff(302,plain,
sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),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(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)],[301,297,294,291]) ).
tff(303,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),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,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)],[302]) ).
tff(304,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,x8),sep(lseg(x13,x6),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(x13,x6),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(305,plain,
sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x13,x8),sep(lseg(x13,x6),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(x13,x6),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)],[304,7]) ).
tff(306,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x13,x6),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(x13,x6),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)],[305]) ).
tff(307,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x13,x6),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(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)],[300]) ).
tff(308,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),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(x13,x6),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)],[307]) ).
tff(309,plain,
sep(lseg(x2,x13),sep(lseg(x14,x12),sep(lseg(x13,x6),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(x13,x6),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)],[308]) ).
tff(310,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),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(x3,x14),sep(lseg(x13,x8),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)],[296]) ).
tff(311,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),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(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)],[310]) ).
tff(312,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(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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(x3,x14),sep(lseg(x13,x8),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(313,plain,
sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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(x3,x14),sep(lseg(x13,x8),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)],[312,7]) ).
tff(314,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x6),sep(lseg(x3,x14),sep(lseg(x13,x8),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)],[313]) ).
tff(315,plain,
sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),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(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)],[314,311]) ).
tff(316,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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,x6),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)],[315]) ).
tff(317,plain,
sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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(transitivity,[status(thm)],[316,309,306,303,273,270,267]) ).
tff(318,plain,
sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),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(monotonicity,[status(thm)],[223,317]) ).
tff(319,plain,
sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),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,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)],[318,260,257,237,240,246,243,227,81,78,63,60,10]) ).
tff(320,plain,
( heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),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)],[319]) ).
tff(321,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,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),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)],[320]) ).
tff(322,plain,
heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))),
inference(modus_ponens,[status(thm)],[155,321]) ).
tff(323,plain,
( ( x2 = x3 )
<=> ( x10 = x3 ) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(324,plain,
( ( x2 = x3 )
<=> ( x3 = x10 ) ),
inference(transitivity,[status(thm)],[323,157]) ).
tff(325,plain,
( ( x3 = x10 )
<=> ( x2 = x3 ) ),
inference(symmetry,[status(thm)],[324]) ).
tff(326,plain,
( ( x3 != x10 )
<=> ( x2 != x3 ) ),
inference(monotonicity,[status(thm)],[325]) ).
tff(327,plain,
x2 != x3,
inference(modus_ponens,[status(thm)],[162,326]) ).
tff(328,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 = x13 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),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 = x13 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(329,plain,
( ( ( x2 = x13 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) )
<=> ( ( x2 = x3 )
| ( x2 = x13 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(330,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,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),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 = x13 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),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)],[329]) ).
tff(331,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,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),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 = x13 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) ) ),
inference(transitivity,[status(thm)],[330,328]) ).
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,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),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(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 = x3 )
| ( x2 = x13 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[332,331]) ).
tff(334,plain,
( ( x2 = x3 )
| ( x2 = x13 )
| ~ heap(sep(lseg(x2,x3),sep(lseg(x2,x13),sep(lseg(x13,x6),sep(lseg(x14,x12),sep(lseg(x3,x14),sep(lseg(x13,x8),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)],[333,173]) ).
tff(335,plain,
x2 = x13,
inference(unit_resolution,[status(thm)],[334,327,322]) ).
tff(336,plain,
lseg(x2,x8) = lseg(x13,x8),
inference(monotonicity,[status(thm)],[335]) ).
tff(337,plain,
sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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(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)],[336,225]) ).
tff(338,plain,
sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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)],[337,22,19,10]) ).
tff(339,plain,
( heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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)],[338]) ).
tff(340,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(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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)],[339]) ).
tff(341,plain,
heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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)],[155,340]) ).
tff(342,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(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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))) )
| ( x2 = x3 )
| ( x2 = x8 )
| ~ heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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(343,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(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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(344,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(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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)],[343,342]) ).
tff(345,plain,
( ( x2 = x8 )
| ~ heap(sep(lseg(x2,x8),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x2,x13),sep(lseg(x10,x2),sep(lseg(x13,x6),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)],[344,173,327]) ).
tff(346,plain,
x2 = x8,
inference(unit_resolution,[status(thm)],[345,341]) ).
tff(347,plain,
x8 = x2,
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
x13 = x2,
inference(symmetry,[status(thm)],[335]) ).
tff(349,plain,
x13 = x10,
inference(transitivity,[status(thm)],[348,179]) ).
tff(350,plain,
lseg(x13,x8) = lseg(x10,x2),
inference(monotonicity,[status(thm)],[349,347]) ).
tff(351,plain,
lseg(x10,x2) = lseg(x13,x8),
inference(symmetry,[status(thm)],[350]) ).
tff(352,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(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)],[351,192]) ).
tff(353,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)],[196]) ).
tff(354,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(355,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)],[354,7]) ).
tff(356,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)],[355]) ).
tff(357,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)],[356,353]) ).
tff(358,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)],[357]) ).
tff(359,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(360,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)],[359,7]) ).
tff(361,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)],[360]) ).
tff(362,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(363,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)],[362,7]) ).
tff(364,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)],[195,31]) ).
tff(365,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)],[364]) ).
tff(366,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)],[365,363]) ).
tff(367,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)],[366]) ).
tff(368,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)],[367]) ).
tff(369,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(370,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)],[369,7]) ).
tff(371,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)],[370]) ).
tff(372,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(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)],[180]) ).
tff(373,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(374,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)],[373,188]) ).
tff(375,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)],[374]) ).
tff(376,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(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)],[375,372,371,368]) ).
tff(377,plain,
lseg(x13,x6) = lseg(x2,x6),
inference(monotonicity,[status(thm)],[348]) ).
tff(378,plain,
lseg(x2,x6) = lseg(x13,x6),
inference(symmetry,[status(thm)],[377]) ).
tff(379,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)],[195]) ).
tff(380,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(381,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)],[380,7]) ).
tff(382,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)],[381]) ).
tff(383,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)],[382,379,50]) ).
tff(384,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)],[383]) ).
tff(385,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(386,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)],[385,7]) ).
tff(387,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)],[386]) ).
tff(388,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)],[387,384]) ).
tff(389,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)],[388]) ).
tff(390,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(391,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)],[390,7]) ).
tff(392,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)],[391]) ).
tff(393,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(394,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)],[393,7]) ).
tff(395,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)],[394]) ).
tff(396,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)],[395,212]) ).
tff(397,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)],[396]) ).
tff(398,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)],[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,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(400,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)],[399,7]) ).
tff(401,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)],[400]) ).
tff(402,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)],[401,398]) ).
tff(403,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)],[402]) ).
tff(404,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(405,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)],[404,7]) ).
tff(406,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)],[405]) ).
tff(407,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)],[406,403]) ).
tff(408,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)],[223,407]) ).
tff(409,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(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)],[408,392,389]) ).
tff(410,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(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)],[378,409]) ).
tff(411,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)],[410,63,60,10]) ).
tff(412,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)],[411]) ).
tff(413,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)],[412]) ).
tff(414,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)],[155,413]) ).
tff(415,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(416,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(417,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)],[416,415]) ).
tff(418,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)],[417,173,327]) ).
tff(419,plain,
x2 = x6,
inference(unit_resolution,[status(thm)],[418,414]) ).
tff(420,plain,
x6 = x2,
inference(symmetry,[status(thm)],[419]) ).
tff(421,plain,
lseg(x2,x6) = lseg(x10,x2),
inference(monotonicity,[status(thm)],[179,420]) ).
tff(422,plain,
lseg(x10,x2) = lseg(x2,x6),
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
lseg(x10,x2) = lseg(x13,x6),
inference(transitivity,[status(thm)],[422,378]) ).
tff(424,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(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)],[423,376]) ).
tff(425,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)],[365]) ).
tff(426,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)],[363]) ).
tff(427,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)],[277]) ).
tff(428,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)],[427]) ).
tff(429,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(430,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)],[429,7]) ).
tff(431,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)],[430]) ).
tff(432,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)],[431,428]) ).
tff(433,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)],[432]) ).
tff(434,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)],[433]) ).
tff(435,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)],[434]) ).
tff(436,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)],[435]) ).
tff(437,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(438,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)],[437,7]) ).
tff(439,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)],[438]) ).
tff(440,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)],[439,436]) ).
tff(441,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)],[180,440]) ).
tff(442,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(443,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)],[442,188]) ).
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(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)],[443]) ).
tff(445,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(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)],[435,438,444,441,426,425]) ).
tff(446,plain,
lseg(x2,x13) = lseg(x10,x2),
inference(monotonicity,[status(thm)],[179,348]) ).
tff(447,plain,
lseg(x10,x2) = lseg(x2,x13),
inference(symmetry,[status(thm)],[446]) ).
tff(448,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(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)],[447,445]) ).
tff(449,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(450,plain,
sep(lseg(x6,x14),sep(lseg(x6,x16),emp)) = sep(lseg(x6,x16),sep(lseg(x6,x14),emp)),
inference(unit_resolution,[status(thm)],[449,7]) ).
tff(451,plain,
sep(lseg(x6,x16),sep(lseg(x6,x14),emp)) = sep(lseg(x6,x14),sep(lseg(x6,x16),emp)),
inference(symmetry,[status(thm)],[450]) ).
tff(452,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)],[451]) ).
tff(453,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(x6,x14),emp))) = sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(454,plain,
sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))),
inference(unit_resolution,[status(thm)],[453,7]) ).
tff(455,plain,
sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x6,x16),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x6,x16),emp))),
inference(transitivity,[status(thm)],[455,452]) ).
tff(457,plain,
sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x11,x4),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)],[456]) ).
tff(458,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(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(459,plain,
sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(unit_resolution,[status(thm)],[458,7]) ).
tff(460,plain,
sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x6,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[459]) ).
tff(461,plain,
sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x11,x4),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)],[460,457]) ).
tff(462,plain,
sep(lseg(x10,x3),sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),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)],[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(x6,x16),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(464,plain,
sep(lseg(x10,x3),sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[463,7]) ).
tff(465,plain,
sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x6,x16),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[464]) ).
tff(466,plain,
sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),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)],[465,462]) ).
tff(467,plain,
sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),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(monotonicity,[status(thm)],[466]) ).
tff(468,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(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(469,plain,
sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[468,7]) ).
tff(470,plain,
sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x3,x14),sep(lseg(x6,x16),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[469]) ).
tff(471,plain,
sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),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)],[470,467,431,428]) ).
tff(472,plain,
sep(lseg(x7,x2),sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),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(monotonicity,[status(thm)],[471]) ).
tff(473,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(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(474,plain,
sep(lseg(x7,x2),sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[473,7]) ).
tff(475,plain,
sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x7,x2),sep(lseg(x6,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[474]) ).
tff(476,plain,
sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),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)],[475,472]) ).
tff(477,plain,
sep(lseg(x14,x12),sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),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)],[476]) ).
tff(478,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(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x6,x16),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),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(479,plain,
sep(lseg(x14,x12),sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x6,x16),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),emp)))))))),
inference(unit_resolution,[status(thm)],[478,7]) ).
tff(480,plain,
sep(lseg(x6,x16),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),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x6,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))),
inference(symmetry,[status(thm)],[479]) ).
tff(481,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),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),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(482,plain,
sep(lseg(x2,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),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),emp)))))),
inference(unit_resolution,[status(thm)],[481,188]) ).
tff(483,plain,
sep(lseg(x2,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[180]) ).
tff(484,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x2,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[483]) ).
tff(485,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),emp)) = sep(lseg(x6,x14),sep(lseg(x11,x4),emp)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(486,plain,
sep(lseg(x11,x4),sep(lseg(x6,x14),emp)) = sep(lseg(x6,x14),sep(lseg(x11,x4),emp)),
inference(unit_resolution,[status(thm)],[485,7]) ).
tff(487,plain,
sep(lseg(x6,x14),sep(lseg(x11,x4),emp)) = sep(lseg(x11,x4),sep(lseg(x6,x14),emp)),
inference(symmetry,[status(thm)],[486]) ).
tff(488,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),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(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(490,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),emp))),
inference(unit_resolution,[status(thm)],[489,7]) ).
tff(491,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),emp))) = sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x11,x4),emp)) = sep(lseg(x11,x4),sep(lseg(x7,x16),emp)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(493,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),emp)) = sep(lseg(x11,x4),sep(lseg(x7,x16),emp)),
inference(unit_resolution,[status(thm)],[492,7]) ).
tff(494,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),emp)) = sep(lseg(x7,x16),sep(lseg(x11,x4),emp)),
inference(symmetry,[status(thm)],[493]) ).
tff(495,plain,
sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),emp))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),emp))),
inference(monotonicity,[status(thm)],[494]) ).
tff(496,plain,
sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),emp))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))),
inference(transitivity,[status(thm)],[495,491,488]) ).
tff(497,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[496]) ).
tff(498,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(x11,x4),sep(lseg(x7,x16),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(499,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),emp)))),
inference(unit_resolution,[status(thm)],[498,7]) ).
tff(500,plain,
sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),emp)))) = sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),emp)))),
inference(symmetry,[status(thm)],[499]) ).
tff(501,plain,
sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),emp))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),emp))),
inference(monotonicity,[status(thm)],[494]) ).
tff(502,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),emp))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),emp))),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),emp)))),
inference(monotonicity,[status(thm)],[502]) ).
tff(504,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),emp))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(505,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),emp))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))),
inference(unit_resolution,[status(thm)],[504,7]) ).
tff(506,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),emp))),
inference(symmetry,[status(thm)],[505]) ).
tff(507,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),emp)))),
inference(monotonicity,[status(thm)],[506]) ).
tff(508,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[507,503,500,497]) ).
tff(509,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[508]) ).
tff(510,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(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(511,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))),
inference(unit_resolution,[status(thm)],[510,7]) ).
tff(512,plain,
sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))) = sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))),
inference(symmetry,[status(thm)],[511]) ).
tff(513,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(x10,x3),sep(lseg(x11,x4),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(514,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp)))),
inference(unit_resolution,[status(thm)],[513,7]) ).
tff(515,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))),
inference(monotonicity,[status(thm)],[514]) ).
tff(516,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(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(517,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))),
inference(unit_resolution,[status(thm)],[516,7]) ).
tff(518,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(x11,x4),emp))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(519,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),emp))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))),
inference(unit_resolution,[status(thm)],[518,7]) ).
tff(520,plain,
sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),emp))),
inference(symmetry,[status(thm)],[519]) ).
tff(521,plain,
sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),emp)))),
inference(monotonicity,[status(thm)],[520]) ).
tff(522,plain,
sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp)))),
inference(symmetry,[status(thm)],[521]) ).
tff(523,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),emp)) = sep(lseg(x11,x4),sep(lseg(x3,x14),emp)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(524,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),emp)) = sep(lseg(x11,x4),sep(lseg(x3,x14),emp)),
inference(unit_resolution,[status(thm)],[523,7]) ).
tff(525,plain,
sep(lseg(x11,x4),sep(lseg(x3,x14),emp)) = sep(lseg(x3,x14),sep(lseg(x11,x4),emp)),
inference(symmetry,[status(thm)],[524]) ).
tff(526,plain,
sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),emp))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),emp))),
inference(monotonicity,[status(thm)],[525]) ).
tff(527,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),emp))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),emp))),
inference(symmetry,[status(thm)],[526]) ).
tff(528,plain,
sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),emp)))),
inference(monotonicity,[status(thm)],[527]) ).
tff(529,plain,
sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),emp)))),
inference(symmetry,[status(thm)],[528]) ).
tff(530,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(x11,x4),sep(lseg(x3,x14),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(531,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x3,x14),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x3,x14),emp)))),
inference(unit_resolution,[status(thm)],[530,7]) ).
tff(532,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(533,plain,
sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))),
inference(unit_resolution,[status(thm)],[532,7]) ).
tff(534,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(535,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),emp)) = sep(lseg(x6,x14),sep(lseg(x3,x14),emp)),
inference(unit_resolution,[status(thm)],[534,7]) ).
tff(536,plain,
sep(lseg(x6,x14),sep(lseg(x3,x14),emp)) = sep(lseg(x3,x14),sep(lseg(x6,x14),emp)),
inference(symmetry,[status(thm)],[535]) ).
tff(537,plain,
sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))),
inference(monotonicity,[status(thm)],[536]) ).
tff(538,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(x3,x14),emp))) = sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x3,x14),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(539,plain,
sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))) = sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x3,x14),emp))),
inference(unit_resolution,[status(thm)],[538,7]) ).
tff(540,plain,
sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x3,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))),
inference(symmetry,[status(thm)],[539]) ).
tff(541,plain,
sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x3,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))),
inference(transitivity,[status(thm)],[540,537,533]) ).
tff(542,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[541]) ).
tff(543,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x11,x4),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[542]) ).
tff(544,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp)))),
inference(transitivity,[status(thm)],[543,531,529,522]) ).
tff(545,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x11,x4),emp))))),
inference(monotonicity,[status(thm)],[544]) ).
tff(546,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(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(547,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[546,7]) ).
tff(548,plain,
sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))),
inference(symmetry,[status(thm)],[537]) ).
tff(549,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[533]) ).
tff(550,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))),
inference(transitivity,[status(thm)],[549,548]) ).
tff(551,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(monotonicity,[status(thm)],[550]) ).
tff(552,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(554,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(unit_resolution,[status(thm)],[553,7]) ).
tff(555,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)],[536]) ).
tff(556,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)],[555]) ).
tff(557,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(monotonicity,[status(thm)],[556]) ).
tff(558,plain,
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),emp)))),
inference(transitivity,[status(thm)],[557,554,552]) ).
tff(559,plain,
sep(lseg(x10,x3),sep(lseg(x11,x4),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(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[558]) ).
tff(560,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[557]) ).
tff(561,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[554]) ).
tff(562,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[561,560]) ).
tff(563,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[562]) ).
tff(564,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[563,559,547,545,517,515,512,509]) ).
tff(565,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),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),emp)))))),
inference(monotonicity,[status(thm)],[564]) ).
tff(566,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(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(567,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[566,7]) ).
tff(568,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,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)],[562]) ).
tff(569,plain,
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(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(symmetry,[status(thm)],[568]) ).
tff(570,plain,
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(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(monotonicity,[status(thm)],[569]) ).
tff(571,plain,
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(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[570,567,565]) ).
tff(572,plain,
sep(lseg(x10,x2),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(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[571]) ).
tff(573,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(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(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(574,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),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(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)],[573,7]) ).
tff(575,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[551,561,560]) ).
tff(576,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),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)],[575]) ).
tff(577,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(x3,x14),sep(lseg(x11,x4),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),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(578,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),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),emp))))),
inference(unit_resolution,[status(thm)],[577,7]) ).
tff(579,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))) = sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))),
inference(monotonicity,[status(thm)],[487]) ).
tff(580,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))),
inference(symmetry,[status(thm)],[579]) ).
tff(581,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(monotonicity,[status(thm)],[580]) ).
tff(582,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[581]) ).
tff(583,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(584,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(unit_resolution,[status(thm)],[583,7]) ).
tff(585,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))) = sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))),
inference(monotonicity,[status(thm)],[487]) ).
tff(586,plain,
sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))),
inference(symmetry,[status(thm)],[585]) ).
tff(587,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(monotonicity,[status(thm)],[586]) ).
tff(588,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[587,584,582]) ).
tff(589,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[588]) ).
tff(590,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[587]) ).
tff(591,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(symmetry,[status(thm)],[584]) ).
tff(592,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[591,590]) ).
tff(593,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[592]) ).
tff(594,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),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)],[593,589,578,576]) ).
tff(595,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x10,x2),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)],[594]) ).
tff(596,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(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(597,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))),
inference(unit_resolution,[status(thm)],[596,7]) ).
tff(598,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))) = sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[592]) ).
tff(599,plain,
sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))),
inference(symmetry,[status(thm)],[598]) ).
tff(600,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))),
inference(monotonicity,[status(thm)],[599]) ).
tff(601,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[581,591,590]) ).
tff(602,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[601]) ).
tff(603,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(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(604,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[603,7]) ).
tff(605,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[604,602]) ).
tff(606,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[605]) ).
tff(607,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,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(608,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[607,7]) ).
tff(609,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[608]) ).
tff(610,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(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(611,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[610,7]) ).
tff(612,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[611]) ).
tff(613,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[575]) ).
tff(614,plain,
sep(lseg(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[613]) ).
tff(615,plain,
sep(lseg(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[614,612]) ).
tff(616,plain,
sep(lseg(x7,x2),sep(lseg(x10,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(x10,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[615]) ).
tff(617,plain,
sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x2),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)],[616,609,606,600,597,595]) ).
tff(618,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x3),sep(lseg(x10,x2),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)],[617]) ).
tff(619,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(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(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(620,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x10,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(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[619,7]) ).
tff(621,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,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(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[620]) ).
tff(622,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),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),emp)))))),
inference(transitivity,[status(thm)],[621,618,574,572,484,482]) ).
tff(623,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,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(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[622]) ).
tff(624,plain,
sep(lseg(x10,x3),sep(lseg(x10,x2),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(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[618]) ).
tff(625,plain,
sep(lseg(x10,x2),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(x10,x2),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)],[574]) ).
tff(626,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x2),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)],[572]) ).
tff(627,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(transitivity,[status(thm)],[626,625,624,620]) ).
tff(628,plain,
sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x10,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[627]) ).
tff(629,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(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(630,plain,
sep(lseg(x10,x2),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),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))),
inference(unit_resolution,[status(thm)],[629,7]) ).
tff(631,plain,
sep(lseg(x13,x8),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),emp)))))))) = sep(lseg(x10,x2),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),emp)))))))),
inference(monotonicity,[status(thm)],[350]) ).
tff(632,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),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),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(633,plain,
sep(lseg(x13,x8),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),emp)))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))),
inference(unit_resolution,[status(thm)],[632,7]) ).
tff(634,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))) = sep(lseg(x13,x8),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),emp)))))))),
inference(symmetry,[status(thm)],[633]) ).
tff(635,plain,
sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[559,547,545,517,515,512,509]) ).
tff(636,plain,
sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),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),emp)))))),
inference(monotonicity,[status(thm)],[635]) ).
tff(637,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[559]) ).
tff(638,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[547]) ).
tff(639,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[638,637]) ).
tff(640,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[639]) ).
tff(641,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(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(642,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(unit_resolution,[status(thm)],[641,7]) ).
tff(643,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(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(644,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[643,7]) ).
tff(645,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[601]) ).
tff(646,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[645]) ).
tff(647,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[646,644]) ).
tff(648,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[647]) ).
tff(649,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),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),emp)))))),
inference(transitivity,[status(thm)],[648,642,640,636]) ).
tff(650,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[649]) ).
tff(651,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(652,plain,
sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[651,7]) ).
tff(653,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[592]) ).
tff(654,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[653]) ).
tff(655,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(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(656,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))),
inference(unit_resolution,[status(thm)],[655,7]) ).
tff(657,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))),
inference(symmetry,[status(thm)],[656]) ).
tff(658,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[592]) ).
tff(659,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))),
inference(symmetry,[status(thm)],[658]) ).
tff(660,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))),
inference(monotonicity,[status(thm)],[659]) ).
tff(661,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[660,657,654]) ).
tff(662,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[661]) ).
tff(663,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(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(664,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[663,7]) ).
tff(665,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[664]) ).
tff(666,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(monotonicity,[status(thm)],[580]) ).
tff(667,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[666]) ).
tff(668,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(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(669,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(unit_resolution,[status(thm)],[668,7]) ).
tff(670,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(symmetry,[status(thm)],[669]) ).
tff(671,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[670,667]) ).
tff(672,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[671]) ).
tff(673,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))),
inference(symmetry,[status(thm)],[672]) ).
tff(674,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(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(675,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[674,7]) ).
tff(676,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[601]) ).
tff(677,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[676]) ).
tff(678,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))),
inference(transitivity,[status(thm)],[677,675,673]) ).
tff(679,plain,
sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))),
inference(monotonicity,[status(thm)],[678]) ).
tff(680,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[679]) ).
tff(681,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(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(682,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))),
inference(unit_resolution,[status(thm)],[681,7]) ).
tff(683,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))),
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[575]) ).
tff(685,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(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(686,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[685,7]) ).
tff(687,plain,
sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[686]) ).
tff(688,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))) = sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[671]) ).
tff(689,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[688,687,684]) ).
tff(690,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[689]) ).
tff(691,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),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(x13,x8),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))))),
inference(symmetry,[status(thm)],[690]) ).
tff(692,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[691,683,680]) ).
tff(693,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[692]) ).
tff(694,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[579]) ).
tff(695,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),sep(lseg(x11,x4),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(696,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(unit_resolution,[status(thm)],[695,7]) ).
tff(697,plain,
sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(symmetry,[status(thm)],[696]) ).
tff(698,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp))),
inference(symmetry,[status(thm)],[488]) ).
tff(699,plain,
sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(monotonicity,[status(thm)],[698]) ).
tff(700,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,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(701,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))),
inference(unit_resolution,[status(thm)],[700,7]) ).
tff(702,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[701]) ).
tff(703,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[702]) ).
tff(704,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),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(transitivity,[status(thm)],[703,699,697,694,551,561,560]) ).
tff(705,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[704]) ).
tff(706,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(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(707,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[706,7]) ).
tff(708,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[707]) ).
tff(709,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),emp)) = sep(lseg(x6,x14),sep(lseg(x7,x16),emp)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(710,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),emp)) = sep(lseg(x6,x14),sep(lseg(x7,x16),emp)),
inference(unit_resolution,[status(thm)],[709,7]) ).
tff(711,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),emp)) = sep(lseg(x7,x16),sep(lseg(x6,x14),emp)),
inference(symmetry,[status(thm)],[710]) ).
tff(712,plain,
sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))),
inference(monotonicity,[status(thm)],[711]) ).
tff(713,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))),
inference(symmetry,[status(thm)],[712]) ).
tff(714,plain,
sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(monotonicity,[status(thm)],[713]) ).
tff(715,plain,
sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[714]) ).
tff(716,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(717,plain,
sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(unit_resolution,[status(thm)],[716,7]) ).
tff(718,plain,
sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(symmetry,[status(thm)],[717]) ).
tff(719,plain,
sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[718,715]) ).
tff(720,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[719]) ).
tff(721,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[720,708,705]) ).
tff(722,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[721]) ).
tff(723,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(724,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(unit_resolution,[status(thm)],[723,7]) ).
tff(725,plain,
sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[719]) ).
tff(726,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(728,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[727,7]) ).
tff(729,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(monotonicity,[status(thm)],[586]) ).
tff(730,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[729]) ).
tff(731,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(x11,x4),emp)))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(732,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(unit_resolution,[status(thm)],[731,7]) ).
tff(733,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(symmetry,[status(thm)],[732]) ).
tff(734,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x11,x4),emp)))),
inference(monotonicity,[status(thm)],[698]) ).
tff(735,plain,
sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[702]) ).
tff(736,plain,
sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[735,734,733,730]) ).
tff(737,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[736]) ).
tff(738,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[737]) ).
tff(739,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))),
inference(transitivity,[status(thm)],[738,728,726]) ).
tff(740,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(monotonicity,[status(thm)],[739]) ).
tff(741,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(742,plain,
sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))) = sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))),
inference(unit_resolution,[status(thm)],[741,7]) ).
tff(743,plain,
sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[742]) ).
tff(744,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[743]) ).
tff(745,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(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(746,plain,
sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))),
inference(unit_resolution,[status(thm)],[745,7]) ).
tff(747,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[746]) ).
tff(748,plain,
sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[747,744]) ).
tff(749,plain,
sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[748]) ).
tff(750,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(751,plain,
sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[750,7]) ).
tff(752,plain,
sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[751]) ).
tff(753,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(x6,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(754,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))),
inference(unit_resolution,[status(thm)],[753,7]) ).
tff(755,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[754]) ).
tff(756,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[755]) ).
tff(757,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[756]) ).
tff(758,plain,
sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[757]) ).
tff(759,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))) = sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))),
inference(monotonicity,[status(thm)],[711]) ).
tff(760,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))),
inference(symmetry,[status(thm)],[759]) ).
tff(761,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(monotonicity,[status(thm)],[760]) ).
tff(762,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[761]) ).
tff(763,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(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(764,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(unit_resolution,[status(thm)],[763,7]) ).
tff(765,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(symmetry,[status(thm)],[764]) ).
tff(766,plain,
sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[765,762]) ).
tff(767,plain,
sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) = sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[766]) ).
tff(768,plain,
sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))),
inference(transitivity,[status(thm)],[767,758,752,749]) ).
tff(769,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[768]) ).
tff(770,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,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(771,plain,
sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(unit_resolution,[status(thm)],[770,7]) ).
tff(772,plain,
sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x11,x4),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(symmetry,[status(thm)],[771]) ).
tff(773,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[766]) ).
tff(774,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))),
inference(symmetry,[status(thm)],[773]) ).
tff(775,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[757]) ).
tff(776,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[775]) ).
tff(777,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,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(778,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[777,7]) ).
tff(779,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(780,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)],[779,7]) ).
tff(781,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)],[780]) ).
tff(782,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)],[781]) ).
tff(783,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(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(784,plain,
sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp)))),
inference(unit_resolution,[status(thm)],[783,7]) ).
tff(785,plain,
sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x7,x2),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)],[784]) ).
tff(786,plain,
sep(lseg(x3,x14),sep(lseg(x7,x16),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(transitivity,[status(thm)],[785,782]) ).
tff(787,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[786]) ).
tff(788,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[787]) ).
tff(789,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))),
inference(transitivity,[status(thm)],[788,778,776,774]) ).
tff(790,plain,
sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x11,x4),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(monotonicity,[status(thm)],[789]) ).
tff(791,plain,
sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[790,772,769,740,724,722]) ).
tff(792,plain,
sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[791]) ).
tff(793,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(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(794,plain,
sep(lseg(x11,x4),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x10,x3),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[793,7]) ).
tff(795,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),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(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(monotonicity,[status(thm)],[789]) ).
tff(796,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[795]) ).
tff(797,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,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(798,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(unit_resolution,[status(thm)],[797,7]) ).
tff(799,plain,
sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(symmetry,[status(thm)],[798]) ).
tff(800,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(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(801,plain,
sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) = sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))),
inference(unit_resolution,[status(thm)],[800,7]) ).
tff(802,plain,
sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(monotonicity,[status(thm)],[801]) ).
tff(803,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(symmetry,[status(thm)],[802]) ).
tff(804,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(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(805,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(unit_resolution,[status(thm)],[804,7]) ).
tff(806,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(807,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)],[806,7]) ).
tff(808,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)],[807]) ).
tff(809,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))) = sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))),
inference(monotonicity,[status(thm)],[711]) ).
tff(810,plain,
sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))),
inference(transitivity,[status(thm)],[809,808]) ).
tff(811,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[810]) ).
tff(812,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(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(813,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(unit_resolution,[status(thm)],[812,7]) ).
tff(814,plain,
sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(symmetry,[status(thm)],[813]) ).
tff(815,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))),
inference(monotonicity,[status(thm)],[711]) ).
tff(816,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))),
inference(symmetry,[status(thm)],[815]) ).
tff(817,plain,
sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),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(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(819,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))),
inference(unit_resolution,[status(thm)],[818,7]) ).
tff(820,plain,
sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))),
inference(symmetry,[status(thm)],[819]) ).
tff(821,plain,
sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp)))) = sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[820]) ).
tff(822,plain,
sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[821,817,814,811]) ).
tff(823,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),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(monotonicity,[status(thm)],[822]) ).
tff(824,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,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(825,plain,
sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[824,7]) ).
tff(826,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x3,x14),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))))),
inference(symmetry,[status(thm)],[825]) ).
tff(827,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp)))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[820]) ).
tff(828,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[827]) ).
tff(829,plain,
sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x10,x3),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[828]) ).
tff(830,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(monotonicity,[status(thm)],[816]) ).
tff(831,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(symmetry,[status(thm)],[830]) ).
tff(832,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(833,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(unit_resolution,[status(thm)],[832,7]) ).
tff(834,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))),
inference(symmetry,[status(thm)],[833]) ).
tff(835,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))) = sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[834,831]) ).
tff(836,plain,
sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp))))) = sep(lseg(x3,x14),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[835]) ).
tff(837,plain,
sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),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)],[836,829,826,823]) ).
tff(838,plain,
sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),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)],[837]) ).
tff(839,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(x3,x14),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(symmetry,[status(thm)],[838]) ).
tff(840,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(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[839,805,803,799,796]) ).
tff(841,plain,
sep(lseg(x11,x4),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(x11,x4),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[840]) ).
tff(842,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(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))) = sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(843,plain,
sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))) = sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))),
inference(unit_resolution,[status(thm)],[842,7]) ).
tff(844,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(x3,x14),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(845,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))),
inference(unit_resolution,[status(thm)],[844,7]) ).
tff(846,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(x3,x14),emp))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(847,plain,
sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))) = sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))),
inference(unit_resolution,[status(thm)],[846,7]) ).
tff(848,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))),
inference(symmetry,[status(thm)],[847]) ).
tff(849,plain,
sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))) = sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))),
inference(transitivity,[status(thm)],[848,555]) ).
tff(850,plain,
sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(monotonicity,[status(thm)],[849]) ).
tff(851,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x3),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[850]) ).
tff(852,plain,
sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))),
inference(transitivity,[status(thm)],[851,845]) ).
tff(853,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(x6,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))),
inference(monotonicity,[status(thm)],[852]) ).
tff(854,plain,
sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))),
inference(transitivity,[status(thm)],[853,843]) ).
tff(855,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(x6,x14),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))),
inference(monotonicity,[status(thm)],[854]) ).
tff(856,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),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)],[855]) ).
tff(857,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(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(858,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[857,7]) ).
tff(859,plain,
sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) = sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))),
inference(symmetry,[status(thm)],[858]) ).
tff(860,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(861,plain,
sep(lseg(x2,x2),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[860,188]) ).
tff(862,plain,
sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),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(transitivity,[status(thm)],[859,856]) ).
tff(863,plain,
sep(lseg(x2,x2),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),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(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[180,862]) ).
tff(864,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(x6,x14),emp))))))) = sep(lseg(x2,x2),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))))),
inference(symmetry,[status(thm)],[863]) ).
tff(865,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(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(transitivity,[status(thm)],[864,861,859,856]) ).
tff(866,plain,
sep(lseg(x11,x4),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(x6,x14),emp)))))))) = sep(lseg(x11,x4),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)],[865]) ).
tff(867,plain,
sep(lseg(x11,x4),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(x6,x14),emp)))))))) = sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(transitivity,[status(thm)],[866,841,794,792,693,665,662,652,650]) ).
tff(868,plain,
sep(lseg(x14,x12),sep(lseg(x11,x4),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(x6,x14),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[867]) ).
tff(869,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x4),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(x6,x14),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x11,x4),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(x6,x14),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(870,plain,
sep(lseg(x11,x4),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(x6,x14),emp))))))))) = sep(lseg(x14,x12),sep(lseg(x11,x4),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(x6,x14),emp))))))))),
inference(unit_resolution,[status(thm)],[869,7]) ).
tff(871,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(x6,x14),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(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[865]) ).
tff(872,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(x6,x14),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(x6,x14),emp)))))))),
inference(symmetry,[status(thm)],[871]) ).
tff(873,plain,
sep(lseg(x11,x4),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(x6,x14),emp)))))))) = sep(lseg(x11,x4),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(x6,x14),emp))))))))),
inference(monotonicity,[status(thm)],[872]) ).
tff(874,plain,
sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))) = sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x16),emp)))))),
inference(symmetry,[status(thm)],[805]) ).
tff(875,plain,
sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),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(transitivity,[status(thm)],[795,798,802,874,838]) ).
tff(876,plain,
sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),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(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[875]) ).
tff(877,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,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(878,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x10,x3),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[877,7]) ).
tff(879,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(x7,x16),sep(lseg(x3,x14),emp))))) = sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(880,plain,
sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))) = sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))),
inference(unit_resolution,[status(thm)],[879,7]) ).
tff(881,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)],[536]) ).
tff(882,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)],[881]) ).
tff(883,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)],[882]) ).
tff(884,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)],[883]) ).
tff(885,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(886,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)],[885,7]) ).
tff(887,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)],[886]) ).
tff(888,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(monotonicity,[status(thm)],[556]) ).
tff(889,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x7,x16),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)],[849]) ).
tff(890,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(x7,x16),sep(lseg(x3,x14),emp)))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(891,plain,
sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))) = sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))),
inference(unit_resolution,[status(thm)],[890,7]) ).
tff(892,plain,
sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x2),sep(lseg(x6,x14),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[891]) ).
tff(893,plain,
sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[892,889,888,887,884]) ).
tff(894,plain,
sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[893]) ).
tff(895,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x6,x14),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))),
inference(symmetry,[status(thm)],[894]) ).
tff(896,plain,
sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))),
inference(transitivity,[status(thm)],[895,880]) ).
tff(897,plain,
sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))),
inference(monotonicity,[status(thm)],[896]) ).
tff(898,plain,
sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(symmetry,[status(thm)],[897]) ).
tff(899,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(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) = sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(900,plain,
sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) = sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[899,7]) ).
tff(901,plain,
sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x6,x14),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))),
inference(symmetry,[status(thm)],[900]) ).
tff(902,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))))) = sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(903,plain,
sep(lseg(x2,x2),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))))) = sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[902,188]) ).
tff(904,plain,
sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp)))))) = sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[901,898]) ).
tff(905,plain,
sep(lseg(x2,x2),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[180,904]) ).
tff(906,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x2,x2),sep(lseg(x6,x14),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),emp))))))),
inference(symmetry,[status(thm)],[905]) ).
tff(907,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,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = 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(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(908,plain,
sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = 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(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[907,7]) ).
tff(909,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(x6,x14),emp))))))) = sep(lseg(x10,x2),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[908]) ).
tff(910,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(x3,x14),sep(lseg(x6,x14),emp)))),
inference(transitivity,[status(thm)],[887,884]) ).
tff(911,plain,
sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[910]) ).
tff(912,plain,
sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(monotonicity,[status(thm)],[911]) ).
tff(913,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(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(914,plain,
sep(lseg(x13,x8),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))) = sep(lseg(x10,x2),sep(lseg(x13,x8),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(unit_resolution,[status(thm)],[913,7]) ).
tff(915,plain,
sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[910]) ).
tff(916,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(symmetry,[status(thm)],[915]) ).
tff(917,plain,
sep(lseg(x10,x2),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(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[782]) ).
tff(918,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(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(919,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(unit_resolution,[status(thm)],[918,7]) ).
tff(920,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)],[781]) ).
tff(921,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)],[920]) ).
tff(922,plain,
sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x3,x14),sep(lseg(x7,x2),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[921]) ).
tff(923,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)],[881]) ).
tff(924,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(925,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)],[924,7]) ).
tff(926,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)],[925]) ).
tff(927,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)],[926,923]) ).
tff(928,plain,
sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))),
inference(monotonicity,[status(thm)],[927]) ).
tff(929,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(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(930,plain,
sep(lseg(x7,x2),sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))) = sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(unit_resolution,[status(thm)],[929,7]) ).
tff(931,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(932,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)],[931,7]) ).
tff(933,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)],[555]) ).
tff(934,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(symmetry,[status(thm)],[933]) ).
tff(935,plain,
sep(lseg(x10,x2),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))) = sep(lseg(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp)))),
inference(transitivity,[status(thm)],[934,932]) ).
tff(936,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(x7,x16),sep(lseg(x10,x2),sep(lseg(x6,x14),sep(lseg(x3,x14),emp))))),
inference(monotonicity,[status(thm)],[935]) ).
tff(937,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(x6,x14),sep(lseg(x3,x14),emp))))),
inference(transitivity,[status(thm)],[936,930,928,922,919,917,916]) ).
tff(938,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(x6,x14),sep(lseg(x3,x14),emp)))))),
inference(monotonicity,[status(thm)],[937]) ).
tff(939,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,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[938,914,912]) ).
tff(940,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,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[939]) ).
tff(941,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,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))),
inference(transitivity,[status(thm)],[940,909,906,903,901,898]) ).
tff(942,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,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[941]) ).
tff(943,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(x14,x12),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(transitivity,[status(thm)],[942,878,876]) ).
tff(944,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(x14,x12),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)],[943]) ).
tff(945,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(946,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)],[945,7]) ).
tff(947,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)],[946]) ).
tff(948,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,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[941]) ).
tff(949,plain,
sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),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)],[948]) ).
tff(950,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,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(951,plain,
sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(unit_resolution,[status(thm)],[950,7]) ).
tff(952,plain,
sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x11,x4),sep(lseg(x14,x12),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[951]) ).
tff(953,plain,
sep(lseg(x14,x12),sep(lseg(x11,x4),sep(lseg(x13,x8),sep(lseg(x7,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))) = sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(monotonicity,[status(thm)],[791]) ).
tff(954,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),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,x16),sep(lseg(x7,x2),sep(lseg(x3,x14),sep(lseg(x6,x14),emp))))))),
inference(symmetry,[status(thm)],[953]) ).
tff(955,plain,
sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),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)],[954,952,949]) ).
tff(956,plain,
sep(lseg(x10,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),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)],[955]) ).
tff(957,plain,
sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),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(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[223]) ).
tff(958,plain,
sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),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(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp))))))),
inference(transitivity,[status(thm)],[957,956,947,944,873,870,868,634,631,630,628,623]) ).
tff(959,plain,
lseg(x2,x16) = lseg(x6,x16),
inference(monotonicity,[status(thm)],[419]) ).
tff(960,plain,
sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),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(x7,x2),sep(lseg(x3,x14),sep(lseg(x10,x3),sep(lseg(x7,x16),sep(lseg(x11,x4),sep(lseg(x6,x14),emp)))))))),
inference(monotonicity,[status(thm)],[959,958]) ).
tff(961,plain,
sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),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)],[960,480,477,435,438,444,441,448,367,370,424,361,358,36,39,44,352,22,19,10]) ).
tff(962,plain,
( heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),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)],[961]) ).
tff(963,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(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ),
inference(symmetry,[status(thm)],[962]) ).
tff(964,plain,
heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))),
inference(modus_ponens,[status(thm)],[155,963]) ).
tff(965,plain,
( ( x2 != x16 )
<=> ( x2 != x16 ) ),
inference(rewrite,[status(thm)],]) ).
tff(966,axiom,
x2 != x16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_8) ).
tff(967,plain,
x2 != x16,
inference(modus_ponens,[status(thm)],[966,965]) ).
tff(968,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(x7,x2),sep(lseg(x13,x8),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(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(969,plain,
( ( ( x2 = x3 )
| ( x2 = x16 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),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(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(970,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(x7,x2),sep(lseg(x13,x8),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(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ) ),
inference(monotonicity,[status(thm)],[969]) ).
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(x7,x2),sep(lseg(x13,x8),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(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ) ),
inference(transitivity,[status(thm)],[970,968]) ).
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(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ),
inference(quant_inst,[status(thm)],]) ).
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 = x16 )
| ( x2 = x3 )
| ~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))) ),
inference(modus_ponens,[status(thm)],[972,971]) ).
tff(974,plain,
~ heap(sep(lseg(x2,x16),sep(lseg(x2,x3),sep(lseg(x14,x12),sep(lseg(x7,x2),sep(lseg(x13,x8),sep(lseg(x11,x4),sep(lseg(x7,x16),sep(lseg(x3,x14),sep(lseg(x6,x14),emp)))))))))),
inference(unit_resolution,[status(thm)],[973,173,967,327]) ).
tff(975,plain,
$false,
inference(unit_resolution,[status(thm)],[974,964]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW438-1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 17:13:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 6.56/4.45 % SZS status Unsatisfiable
% 6.56/4.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------