TSTP Solution File: SWW443-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW443-1 : 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 20:58:42 EDT 2022
% Result : Unsatisfiable 8.03s 5.36s
% Output : Proof 8.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 140
% Syntax : Number of formulae : 642 ( 479 unt; 18 typ; 0 def)
% Number of atoms : 899 ( 806 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 465 ( 194 ~; 234 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 15 ( 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 : 17 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 454 ( 441 !; 0 ?; 454 :)
% Comments :
%------------------------------------------------------------------------------
tff(heap_type,type,
heap: $i > $o ).
tff(sep_type,type,
sep: ( $i * $i ) > $i ).
tff(emp_type,type,
emp: $i ).
tff(lseg_type,type,
lseg: ( $i * $i ) > $i ).
tff(x7_type,type,
x7: $i ).
tff(x11_type,type,
x11: $i ).
tff(x9_type,type,
x9: $i ).
tff(x5_type,type,
x5: $i ).
tff(x18_type,type,
x18: $i ).
tff(x2_type,type,
x2: $i ).
tff(x14_type,type,
x14: $i ).
tff(x1_type,type,
x1: $i ).
tff(x3_type,type,
x3: $i ).
tff(x15_type,type,
x15: $i ).
tff(x10_type,type,
x10: $i ).
tff(x13_type,type,
x13: $i ).
tff(x12_type,type,
x12: $i ).
tff(x8_type,type,
x8: $i ).
tff(1,plain,
^ [Sigma: $i,S: $i,T: $i] :
refl(
( ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',associative_commutative) ).
tff(5,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,plain,
sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[14,11]) ).
tff(16,plain,
sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[20,7]) ).
tff(22,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[22,19]) ).
tff(24,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(transitivity,[status(thm)],[34,28]) ).
tff(36,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),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(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),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(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[31]) ).
tff(44,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[46,7]) ).
tff(48,plain,
sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[55,52]) ).
tff(57,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[58,7]) ).
tff(60,plain,
sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(transitivity,[status(thm)],[60,57,45,42]) ).
tff(62,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(transitivity,[status(thm)],[62,40,37,26]) ).
tff(64,plain,
( heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))))
<=> heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))))
<=> heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))))
<=> heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_23) ).
tff(68,plain,
heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))),
inference(modus_ponens,[status(thm)],[68,65]) ).
tff(70,plain,
( ( x1 != x14 )
<=> ( x1 != x14 ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
x1 != x14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_19) ).
tff(72,plain,
x1 != x14,
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,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(74,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)],[73]) ).
tff(75,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(76,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(77,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)],[76]) ).
tff(78,axiom,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma)))
| ( X = Y )
| ( X = Z ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',wellformedness_5) ).
tff(79,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)],[78,77]) ).
tff(80,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)],[79,75]) ).
tff(81,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)],[80]) ).
tff(82,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)],[81,74]) ).
tff(83,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x1 = x14 )
| ( x1 = x3 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x1 = x14 )
| ( x1 = x3 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ( x1 = x3 )
| ( x1 = x14 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) )
<=> ( ( x1 = x14 )
| ( x1 = x3 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x1 = x3 )
| ( x1 = x14 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x1 = x14 )
| ( x1 = x3 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x1 = x3 )
| ( x1 = x14 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x1 = x14 )
| ( x1 = x3 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ) ),
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x1 = x3 )
| ( x1 = x14 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x1 = x14 )
| ( x1 = x3 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ( x1 = x3 )
| ~ heap(sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ),
inference(unit_resolution,[status(thm)],[88,82,72]) ).
tff(90,plain,
x1 = x3,
inference(unit_resolution,[status(thm)],[89,69]) ).
tff(91,plain,
x3 = x1,
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
lseg(x3,x3) = lseg(x1,x3),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
sep(lseg(x3,x3),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[92,23]) ).
tff(94,plain,
^ [Sigma: $i,X: $i] :
refl(
( ( sep(lseg(X,X),Sigma) = Sigma )
<=> ( sep(lseg(X,X),Sigma) = Sigma ) )),
inference(bind,[status(th)],]) ).
tff(95,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)],[94]) ).
tff(96,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(97,axiom,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',normalization) ).
tff(98,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
sep(lseg(x3,x3),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x3,x3),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[104,7]) ).
tff(106,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[106,7]) ).
tff(108,plain,
sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x8),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x8),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[110,7]) ).
tff(112,plain,
sep(lseg(x2,x8),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
sep(lseg(x2,x8),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[112,109]) ).
tff(114,plain,
sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[14,11,115,105]) ).
tff(117,plain,
sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[119,7]) ).
tff(121,plain,
sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[121,118]) ).
tff(123,plain,
lseg(x3,x14) = lseg(x1,x14),
inference(monotonicity,[status(thm)],[91]) ).
tff(124,plain,
sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[123,122]) ).
tff(125,plain,
sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[124,103,93]) ).
tff(126,plain,
lseg(x10,x3) = lseg(x10,x1),
inference(monotonicity,[status(thm)],[91]) ).
tff(127,plain,
sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[126,125]) ).
tff(128,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[15]) ).
tff(130,plain,
sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[133,7]) ).
tff(135,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[135,132]) ).
tff(137,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[122]) ).
tff(140,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[131,134,140]) ).
tff(142,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[144,7]) ).
tff(146,plain,
sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[122]) ).
tff(147,plain,
sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[146,22,19]) ).
tff(148,plain,
sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[149,145,143,138]) ).
tff(151,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[153,7]) ).
tff(155,plain,
sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[11]) ).
tff(156,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[156,7]) ).
tff(158,plain,
sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[158,155]) ).
tff(160,plain,
sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[162,7]) ).
tff(164,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[159]) ).
tff(166,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[136]) ).
tff(169,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[168,167,164,161]) ).
tff(170,plain,
sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[130]) ).
tff(173,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[174,7]) ).
tff(176,plain,
sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[176,173]) ).
tff(178,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[179,7]) ).
tff(181,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[181,178]) ).
tff(183,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[184,7]) ).
tff(186,plain,
sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[187,7]) ).
tff(189,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[17]) ).
tff(190,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[191,7]) ).
tff(193,plain,
sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[193,190]) ).
tff(195,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[196,188]) ).
tff(198,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x18),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[10]) ).
tff(200,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(202,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[201,7]) ).
tff(203,plain,
sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[203,200]) ).
tff(205,plain,
sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[209,7]) ).
tff(211,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[211,208]) ).
tff(213,plain,
sep(lseg(x3,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[92,212]) ).
tff(214,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
sep(lseg(x3,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[214,100]) ).
tff(216,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x3,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x18),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[109]) ).
tff(218,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(219,plain,
sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[218,7]) ).
tff(220,plain,
sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[220,217]) ).
tff(222,plain,
sep(lseg(x1,x14),sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(224,plain,
sep(lseg(x1,x14),sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[223,7]) ).
tff(225,plain,
sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[225,222]) ).
tff(227,plain,
sep(lseg(x10,x1),sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[226]) ).
tff(228,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(229,plain,
sep(lseg(x10,x1),sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[228,7]) ).
tff(230,plain,
sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[229]) ).
tff(231,plain,
sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[230,227]) ).
tff(232,plain,
sep(lseg(x18,x15),sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(234,plain,
sep(lseg(x18,x15),sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[233,7]) ).
tff(235,plain,
sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(237,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[236,7]) ).
tff(238,plain,
sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[237]) ).
tff(239,plain,
sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(244,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[243,7]) ).
tff(245,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[238]) ).
tff(247,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(250,plain,
sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[249,7]) ).
tff(251,plain,
sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[251,246]) ).
tff(253,plain,
sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(255,plain,
sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[254,7]) ).
tff(256,plain,
sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(258,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[257,7]) ).
tff(259,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
lseg(x1,x3) = lseg(x3,x3),
inference(symmetry,[status(thm)],[92]) ).
tff(261,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x3,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
sep(lseg(x3,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(264,plain,
sep(lseg(x3,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[263,100]) ).
tff(265,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x3,x3),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[265,262,259]) ).
tff(267,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(269,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[268,7]) ).
tff(270,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[269,267]) ).
tff(271,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[270]) ).
tff(272,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[273,256,253,248,245,242]) ).
tff(275,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(276,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[275,7]) ).
tff(277,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[276]) ).
tff(278,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(280,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[279,7]) ).
tff(281,plain,
sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(transitivity,[status(thm)],[281,278]) ).
tff(283,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(monotonicity,[status(thm)],[282]) ).
tff(284,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(285,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(unit_resolution,[status(thm)],[284,7]) ).
tff(286,plain,
sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[47]) ).
tff(288,plain,
sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(290,plain,
sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[289,7]) ).
tff(291,plain,
sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[291,288]) ).
tff(293,plain,
sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[294]) ).
tff(296,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(298,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[297,7]) ).
tff(299,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[298]) ).
tff(300,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(transitivity,[status(thm)],[299,296]) ).
tff(301,plain,
sep(lseg(x3,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x3),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(monotonicity,[status(thm)],[92,300]) ).
tff(302,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(303,plain,
sep(lseg(x3,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[302,100]) ).
tff(304,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x3,x3),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[288]) ).
tff(306,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(307,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[306,7]) ).
tff(308,plain,
sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[307]) ).
tff(309,plain,
sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[308,305]) ).
tff(310,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[309]) ).
tff(311,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(312,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[311,7]) ).
tff(313,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[312]) ).
tff(314,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(315,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[314,7]) ).
tff(316,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(317,plain,
sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[316,7]) ).
tff(318,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x12),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(319,plain,
sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x12),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[318,7]) ).
tff(320,plain,
sep(lseg(x2,x12),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[321]) ).
tff(323,plain,
sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[48,322,317]) ).
tff(324,plain,
sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[323]) ).
tff(325,plain,
sep(lseg(x18,x15),sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[324]) ).
tff(326,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(327,plain,
sep(lseg(x18,x15),sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[326,7]) ).
tff(328,plain,
sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x12),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[327]) ).
tff(329,plain,
sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[328,325]) ).
tff(330,plain,
sep(lseg(x10,x1),sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(332,plain,
sep(lseg(x10,x1),sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[331,7]) ).
tff(333,plain,
sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[333,330,315]) ).
tff(335,plain,
sep(lseg(x1,x14),sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[334]) ).
tff(336,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(337,plain,
sep(lseg(x1,x14),sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[336,7]) ).
tff(338,plain,
sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(340,plain,
sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[339]) ).
tff(341,plain,
sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[341]) ).
tff(343,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(344,plain,
sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[343,7]) ).
tff(345,plain,
sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[344]) ).
tff(346,plain,
sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[345,342]) ).
tff(347,plain,
sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[346]) ).
tff(348,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[347]) ).
tff(349,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(350,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[349,7]) ).
tff(351,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x9,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(353,plain,
sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x9,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[352,7]) ).
tff(354,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x9,x5),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(355,plain,
sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x9,x5),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[354,7]) ).
tff(356,plain,
sep(lseg(x9,x5),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[356]) ).
tff(358,plain,
sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[357]) ).
tff(359,plain,
sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x9,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[108,358,353]) ).
tff(360,plain,
sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x13),sep(lseg(x9,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[359]) ).
tff(361,plain,
sep(lseg(x12,x13),sep(lseg(x9,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),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(x12,x13),sep(lseg(x9,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(363,plain,
sep(lseg(x12,x13),sep(lseg(x9,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[362,7]) ).
tff(364,plain,
sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x13),sep(lseg(x9,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[364,361]) ).
tff(366,plain,
sep(lseg(x2,x5),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[365]) ).
tff(367,plain,
sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x5),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[366]) ).
tff(368,plain,
sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[367]) ).
tff(369,plain,
sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[368]) ).
tff(370,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(371,plain,
sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[370,7]) ).
tff(372,plain,
sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[372,369]) ).
tff(374,plain,
sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[373]) ).
tff(375,plain,
sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[374,351,348]) ).
tff(376,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[375]) ).
tff(377,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(378,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[377,7]) ).
tff(379,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[373]) ).
tff(381,plain,
sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(383,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[382,7]) ).
tff(384,plain,
sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[346]) ).
tff(385,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[384]) ).
tff(386,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[386,383,381]) ).
tff(388,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x9,x5),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(390,plain,
sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[389,7]) ).
tff(391,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x8),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(392,plain,
sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x8),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[391,7]) ).
tff(393,plain,
sep(lseg(x2,x8),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[392]) ).
tff(394,plain,
sep(lseg(x2,x8),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[393,339]) ).
tff(395,plain,
sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[394]) ).
tff(396,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(397,plain,
sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[396,7]) ).
tff(398,plain,
sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[398,395]) ).
tff(400,plain,
sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[399]) ).
tff(401,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[400]) ).
tff(402,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[401,390]) ).
tff(403,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[402]) ).
tff(404,plain,
sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(406,plain,
sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[405,7]) ).
tff(407,plain,
sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[406]) ).
tff(408,plain,
sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[407,404]) ).
tff(409,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[408]) ).
tff(410,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(411,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[410,7]) ).
tff(412,plain,
sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[411]) ).
tff(413,plain,
sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[412,409,388,379,376]) ).
tff(414,plain,
sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x2,x12),sep(lseg(x1,x14),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[413]) ).
tff(415,plain,
sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(transitivity,[status(thm)],[414,338,335,313,310,295,298,304,301,286,283,26]) ).
tff(416,plain,
( heap(sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))
<=> heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))))
<=> heap(sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ),
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
heap(sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(modus_ponens,[status(thm)],[68,417]) ).
tff(419,plain,
( ( x2 != x8 )
<=> ( x2 != x8 ) ),
inference(rewrite,[status(thm)],]) ).
tff(420,axiom,
x2 != x8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_8) ).
tff(421,plain,
x2 != x8,
inference(modus_ponens,[status(thm)],[420,419]) ).
tff(422,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x8 )
| ( x2 = x12 )
| ~ heap(sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x8 )
| ( x2 = x12 )
| ~ heap(sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(423,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x8 )
| ( x2 = x12 )
| ~ heap(sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(424,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x8 )
| ( x2 = x12 )
| ~ heap(sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ),
inference(modus_ponens,[status(thm)],[423,422]) ).
tff(425,plain,
( ( x2 = x12 )
| ~ heap(sep(lseg(x2,x12),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ),
inference(unit_resolution,[status(thm)],[424,82,421]) ).
tff(426,plain,
x2 = x12,
inference(unit_resolution,[status(thm)],[425,418]) ).
tff(427,plain,
x12 = x2,
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
lseg(x12,x12) = lseg(x2,x12),
inference(monotonicity,[status(thm)],[427]) ).
tff(429,plain,
sep(lseg(x12,x12),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x2,x12),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[428,274]) ).
tff(430,plain,
sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[273]) ).
tff(431,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[253]) ).
tff(432,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[248]) ).
tff(433,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[432,431,255,430]) ).
tff(434,plain,
sep(lseg(x12,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x12,x12),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[433]) ).
tff(435,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x12,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(436,plain,
sep(lseg(x12,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[435,100]) ).
tff(437,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x12),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[436]) ).
tff(438,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))) = sep(lseg(x7,x5),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(439,plain,
sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))) = sep(lseg(x7,x5),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))),
inference(unit_resolution,[status(thm)],[438,7]) ).
tff(440,plain,
sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x18),sep(lseg(x7,x5),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[439]) ).
tff(441,plain,
sep(lseg(x2,x18),sep(lseg(x7,x5),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x7,x5),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[441]) ).
tff(443,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x18),sep(lseg(x7,x5),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(444,plain,
sep(lseg(x2,x18),sep(lseg(x7,x5),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[443,7]) ).
tff(445,plain,
sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x18),sep(lseg(x7,x5),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[444]) ).
tff(446,plain,
sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x7,x5),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[445]) ).
tff(447,plain,
sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[446,442]) ).
tff(448,plain,
sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[447]) ).
tff(449,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(450,plain,
sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[449,7]) ).
tff(451,plain,
sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[450]) ).
tff(452,plain,
sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[451,448]) ).
tff(453,plain,
sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[452]) ).
tff(454,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(455,plain,
sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[454,7]) ).
tff(456,plain,
sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[455]) ).
tff(457,plain,
sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[456,453]) ).
tff(458,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[457]) ).
tff(459,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(460,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[459,7]) ).
tff(461,plain,
sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[460]) ).
tff(462,plain,
sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[461,458]) ).
tff(463,plain,
sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[462]) ).
tff(464,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(465,plain,
sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[464,7]) ).
tff(466,plain,
sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(468,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[467,7]) ).
tff(469,plain,
sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[468]) ).
tff(470,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(471,plain,
sep(lseg(x3,x3),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[470,100]) ).
tff(472,plain,
sep(lseg(x3,x3),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[92,469]) ).
tff(473,plain,
sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x3,x3),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[472]) ).
tff(474,plain,
sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(transitivity,[status(thm)],[473,471,469]) ).
tff(475,plain,
sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[474]) ).
tff(476,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x18),sep(lseg(x11,x9),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x9),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(477,plain,
sep(lseg(x2,x18),sep(lseg(x11,x9),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x9),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[476,7]) ).
tff(478,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))) = sep(lseg(x11,x9),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(479,plain,
sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))) = sep(lseg(x11,x9),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))),
inference(unit_resolution,[status(thm)],[478,7]) ).
tff(480,plain,
sep(lseg(x11,x9),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))) = sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))),
inference(symmetry,[status(thm)],[479]) ).
tff(481,plain,
sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))),
inference(monotonicity,[status(thm)],[480]) ).
tff(482,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))) = sep(lseg(x11,x9),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(483,plain,
sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))) = sep(lseg(x11,x9),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))),
inference(unit_resolution,[status(thm)],[482,7]) ).
tff(484,plain,
sep(lseg(x11,x9),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))),
inference(symmetry,[status(thm)],[483]) ).
tff(485,plain,
sep(lseg(x11,x9),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))) = sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))),
inference(transitivity,[status(thm)],[484,481]) ).
tff(486,plain,
sep(lseg(x2,x18),sep(lseg(x11,x9),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))),
inference(monotonicity,[status(thm)],[485]) ).
tff(487,plain,
sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x2,x18),sep(lseg(x11,x9),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))),
inference(symmetry,[status(thm)],[486]) ).
tff(488,plain,
sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x11,x9),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))),
inference(transitivity,[status(thm)],[445,441,487,477]) ).
tff(489,plain,
sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x12,x13),sep(lseg(x11,x9),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[488]) ).
tff(490,plain,
sep(lseg(x12,x13),sep(lseg(x11,x9),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))) = sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[489]) ).
tff(491,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x13),sep(lseg(x11,x9),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))) = sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(492,plain,
sep(lseg(x12,x13),sep(lseg(x11,x9),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))) = sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))),
inference(unit_resolution,[status(thm)],[491,7]) ).
tff(493,plain,
sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))) = sep(lseg(x12,x13),sep(lseg(x11,x9),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))) = sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[493,490]) ).
tff(495,plain,
sep(lseg(x1,x14),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[494]) ).
tff(496,plain,
sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x14),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[495]) ).
tff(497,plain,
sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[496]) ).
tff(498,plain,
sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[497]) ).
tff(499,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(500,plain,
sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[499,7]) ).
tff(501,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[500]) ).
tff(502,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[501,498]) ).
tff(503,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[502]) ).
tff(504,plain,
sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[503,475]) ).
tff(505,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[504]) ).
tff(506,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(507,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[506,7]) ).
tff(508,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[502]) ).
tff(509,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[508]) ).
tff(510,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[474]) ).
tff(511,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[510]) ).
tff(512,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[511,509]) ).
tff(513,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x11,x9),sep(lseg(x12,x13),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[512]) ).
tff(514,plain,
sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[469]) ).
tff(515,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(516,plain,
sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[515,7]) ).
tff(517,plain,
sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[516]) ).
tff(518,plain,
sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x3,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(monotonicity,[status(thm)],[260]) ).
tff(519,plain,
sep(lseg(x3,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[518]) ).
tff(520,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(521,plain,
sep(lseg(x3,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))),
inference(unit_resolution,[status(thm)],[520,100]) ).
tff(522,plain,
sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x3,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(symmetry,[status(thm)],[521]) ).
tff(523,plain,
sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))) = sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))),
inference(transitivity,[status(thm)],[522,519]) ).
tff(524,plain,
sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(monotonicity,[status(thm)],[523]) ).
tff(525,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[524]) ).
tff(526,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[525]) ).
tff(527,plain,
sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[526]) ).
tff(528,plain,
sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[527,517,514]) ).
tff(529,plain,
sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[528]) ).
tff(530,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(531,plain,
sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[530,7]) ).
tff(532,plain,
sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[531]) ).
tff(533,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(534,plain,
sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(unit_resolution,[status(thm)],[533,7]) ).
tff(535,plain,
sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))) = sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))),
inference(symmetry,[status(thm)],[534]) ).
tff(536,plain,
sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(monotonicity,[status(thm)],[535]) ).
tff(537,plain,
sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[536]) ).
tff(538,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[537]) ).
tff(539,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[538]) ).
tff(540,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(541,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[540,7]) ).
tff(542,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[541]) ).
tff(543,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[542,539]) ).
tff(544,plain,
sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[543]) ).
tff(545,plain,
sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[544,532,529,513,507,505]) ).
tff(546,plain,
lseg(x12,x8) = lseg(x2,x8),
inference(monotonicity,[status(thm)],[427]) ).
tff(547,plain,
sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[546,545]) ).
tff(548,plain,
sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[547,466,463,248,437,434,429,235,232,207,210,216,213,198,186,183,171,154,152,128]) ).
tff(549,plain,
( heap(sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))
<=> heap(sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[548]) ).
tff(550,plain,
( heap(sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))
<=> heap(sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ),
inference(symmetry,[status(thm)],[549]) ).
tff(551,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x12,x12),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(552,plain,
sep(lseg(x12,x12),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[551,100]) ).
tff(553,plain,
lseg(x2,x12) = lseg(x12,x12),
inference(symmetry,[status(thm)],[428]) ).
tff(554,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x2,x5),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(555,plain,
sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x2,x5),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(unit_resolution,[status(thm)],[554,7]) ).
tff(556,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x5),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(557,plain,
sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x5),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[556,7]) ).
tff(558,plain,
sep(lseg(x2,x5),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[557]) ).
tff(559,plain,
sep(lseg(x2,x5),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[558,49,30]) ).
tff(560,plain,
sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[559]) ).
tff(561,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(562,plain,
sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[561,7]) ).
tff(563,plain,
sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x5),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[562]) ).
tff(564,plain,
sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[563,560]) ).
tff(565,plain,
sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(monotonicity,[status(thm)],[564]) ).
tff(566,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x5),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(symmetry,[status(thm)],[565]) ).
tff(567,plain,
sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x2,x5),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(transitivity,[status(thm)],[566,555]) ).
tff(568,plain,
sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(monotonicity,[status(thm)],[567]) ).
tff(569,plain,
sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x12,x13),sep(lseg(x1,x3),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(symmetry,[status(thm)],[568]) ).
tff(570,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(571,plain,
sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(unit_resolution,[status(thm)],[570,7]) ).
tff(572,plain,
sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x5),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(symmetry,[status(thm)],[571]) ).
tff(573,plain,
sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x8),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(symmetry,[status(thm)],[105]) ).
tff(574,plain,
sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))) = sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))),
inference(transitivity,[status(thm)],[573,114]) ).
tff(575,plain,
sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(monotonicity,[status(thm)],[574]) ).
tff(576,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(577,plain,
sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[576,7]) ).
tff(578,plain,
sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x2,x8),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))) = sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))),
inference(transitivity,[status(thm)],[578,575]) ).
tff(580,plain,
sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(monotonicity,[status(thm)],[579]) ).
tff(581,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(582,plain,
sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[581,7]) ).
tff(583,plain,
sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x2,x8),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(symmetry,[status(thm)],[582]) ).
tff(584,plain,
sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))) = sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))),
inference(transitivity,[status(thm)],[583,580]) ).
tff(585,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(monotonicity,[status(thm)],[584]) ).
tff(586,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(587,plain,
sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(unit_resolution,[status(thm)],[586,7]) ).
tff(588,plain,
sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x18,x15),sep(lseg(x2,x8),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(symmetry,[status(thm)],[587]) ).
tff(589,plain,
sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))) = sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(transitivity,[status(thm)],[588,585,207,210,216,213,198,186,183]) ).
tff(590,plain,
sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(monotonicity,[status(thm)],[589]) ).
tff(591,plain,
sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) = sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(transitivity,[status(thm)],[590,572,569,40,37,26]) ).
tff(592,plain,
( heap(sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))
<=> heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))))) ),
inference(monotonicity,[status(thm)],[591]) ).
tff(593,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))))
<=> heap(sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ),
inference(symmetry,[status(thm)],[592]) ).
tff(594,plain,
heap(sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(modus_ponens,[status(thm)],[68,593]) ).
tff(595,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x8 )
| ( x2 = x5 )
| ~ heap(sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x8 )
| ( x2 = x5 )
| ~ heap(sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(596,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x8 )
| ( x2 = x5 )
| ~ heap(sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(597,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x2 = x8 )
| ( x2 = x5 )
| ~ heap(sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ),
inference(modus_ponens,[status(thm)],[596,595]) ).
tff(598,plain,
( ( x2 = x5 )
| ~ heap(sep(lseg(x2,x5),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x14),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) ),
inference(unit_resolution,[status(thm)],[597,82,421]) ).
tff(599,plain,
x2 = x5,
inference(unit_resolution,[status(thm)],[598,594]) ).
tff(600,plain,
x5 = x2,
inference(symmetry,[status(thm)],[599]) ).
tff(601,plain,
x5 = x12,
inference(transitivity,[status(thm)],[600,426]) ).
tff(602,plain,
lseg(x2,x5) = lseg(x2,x12),
inference(monotonicity,[status(thm)],[601]) ).
tff(603,plain,
lseg(x2,x5) = lseg(x12,x12),
inference(transitivity,[status(thm)],[602,553]) ).
tff(604,plain,
sep(lseg(x2,x5),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x12,x12),sep(lseg(x1,x14),sep(lseg(x18,x15),sep(lseg(x10,x1),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))),
inference(monotonicity,[status(thm)],[603]) ).
tff(605,plain,
sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))) = sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))),
inference(transitivity,[status(thm)],[25,36,39,568,571,604,552,171,154,152,128]) ).
tff(606,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x14),sep(lseg(x1,x3),sep(lseg(x12,x13),sep(lseg(x2,x5),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x2,x8),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp))))))))))))))
<=> heap(sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[605]) ).
tff(607,plain,
heap(sep(lseg(x10,x3),sep(lseg(x3,x14),sep(lseg(x2,x8),sep(lseg(x18,x15),sep(lseg(x12,x13),sep(lseg(x2,x12),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x7,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(modus_ponens,[status(thm)],[68,606]) ).
tff(608,plain,
heap(sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))),
inference(modus_ponens,[status(thm)],[607,550]) ).
tff(609,plain,
( ( x12 = x13 )
<=> ( x2 = x13 ) ),
inference(monotonicity,[status(thm)],[427]) ).
tff(610,plain,
( ( x2 = x13 )
<=> ( x12 = x13 ) ),
inference(symmetry,[status(thm)],[609]) ).
tff(611,plain,
( ( x2 != x13 )
<=> ( x12 != x13 ) ),
inference(monotonicity,[status(thm)],[610]) ).
tff(612,plain,
( ( x2 != x13 )
<=> ( x2 != x13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(613,axiom,
x2 != x13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_9) ).
tff(614,plain,
x2 != x13,
inference(modus_ponens,[status(thm)],[613,612]) ).
tff(615,plain,
x12 != x13,
inference(modus_ponens,[status(thm)],[614,611]) ).
tff(616,plain,
( ( x12 = x8 )
<=> ( x2 = x8 ) ),
inference(monotonicity,[status(thm)],[427]) ).
tff(617,plain,
( ( x2 = x8 )
<=> ( x12 = x8 ) ),
inference(symmetry,[status(thm)],[616]) ).
tff(618,plain,
( ( x2 != x8 )
<=> ( x12 != x8 ) ),
inference(monotonicity,[status(thm)],[617]) ).
tff(619,plain,
x12 != x8,
inference(modus_ponens,[status(thm)],[421,618]) ).
tff(620,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x12 = x13 )
| ( x12 = x8 )
| ~ heap(sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x12 = x13 )
| ( x12 = x8 )
| ~ heap(sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(621,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x12 = x13 )
| ( x12 = x8 )
| ~ heap(sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(622,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x12 = x13 )
| ( x12 = x8 )
| ~ heap(sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[621,620]) ).
tff(623,plain,
( ( x12 = x13 )
| ( x12 = x8 )
| ~ heap(sep(lseg(x12,x8),sep(lseg(x12,x13),sep(lseg(x10,x1),sep(lseg(x18,x15),sep(lseg(x1,x3),sep(lseg(x1,x14),sep(lseg(x7,x5),sep(lseg(x2,x18),sep(lseg(x9,x5),sep(lseg(x11,x9),sep(lseg(x11,x7),emp)))))))))))) ),
inference(unit_resolution,[status(thm)],[622,82]) ).
tff(624,plain,
$false,
inference(unit_resolution,[status(thm)],[623,619,615,608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW443-1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 17:18:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 8.03/5.36 % SZS status Unsatisfiable
% 8.03/5.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------