%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW429-1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:58 AM UTC 2025
% Result : Unsatisfiable 7.94s 8.15s
% Output : Proof 8.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 242
% Syntax : Number of formulae : 1380 (1067 unt; 0 typ; 0 def)
% Number of atoms : 2081 (1739 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 1159 ( 464 ~; 608 |; 0 &)
% ( 87 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 1028 (1005 !; 0 ?;1028 :)
% 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(x11_type,type,
x11: $i ).
tff(x8_type,type,
x8: $i ).
tff(x9_type,type,
x9: $i ).
tff(x6_type,type,
x6: $i ).
tff(x7_type,type,
x7: $i ).
tff(x4_type,type,
x4: $i ).
tff(x12_type,type,
x12: $i ).
tff(x3_type,type,
x3: $i ).
tff(x5_type,type,
x5: $i ).
tff(x1_type,type,
x1: $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(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(14,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[13,7]) ).
tff(15,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[10]) ).
tff(17,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[18,15,12]) ).
tff(20,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[21,7]) ).
tff(23,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[17]) ).
tff(25,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[26,7]) ).
tff(28,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[28,25]) ).
tff(30,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[30,23,20]) ).
tff(32,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[33,7]) ).
tff(35,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[29]) ).
tff(36,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))) = sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))) = sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x6,x9),sep(lseg(x8,x11),emp)) = sep(lseg(x8,x11),sep(lseg(x6,x9),emp)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
sep(lseg(x6,x9),sep(lseg(x8,x11),emp)) = sep(lseg(x8,x11),sep(lseg(x6,x9),emp)),
inference(unit_resolution,[status(thm)],[40,7]) ).
tff(42,plain,
sep(lseg(x8,x11),sep(lseg(x6,x9),emp)) = sep(lseg(x6,x9),sep(lseg(x8,x11),emp)),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) = sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))),
inference(transitivity,[status(thm)],[10,44,39]) ).
tff(46,plain,
sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[24,27,49]) ).
tff(51,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),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(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[55,52]) ).
tff(57,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),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(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[58,7]) ).
tff(60,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[61,7]) ).
tff(63,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[11]) ).
tff(64,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[64,7]) ).
tff(66,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[47]) ).
tff(68,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[67,66,63]) ).
tff(69,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[70,62]) ).
tff(72,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[72,60,57,37,34,32]) ).
tff(74,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[75,7]) ).
tff(77,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[77,7]) ).
tff(79,plain,
sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))),
inference(symmetry,[status(thm)],[39]) ).
tff(80,plain,
sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))),
inference(transitivity,[status(thm)],[79,43]) ).
tff(81,plain,
sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(transitivity,[status(thm)],[82,78]) ).
tff(84,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[86,7]) ).
tff(88,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[88,85]) ).
tff(90,plain,
sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[94,7]) ).
tff(96,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[44]) ).
tff(98,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[99,7]) ).
tff(101,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[101,98]) ).
tff(103,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[105,7]) ).
tff(107,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[102]) ).
tff(108,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[89]) ).
tff(111,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[110,109,106,104]) ).
tff(112,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[113,96,93]) ).
tff(115,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[115,76,74]) ).
tff(117,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),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(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[119,7]) ).
tff(121,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[121,110,109,106,104]) ).
tff(123,plain,
sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[124,7]) ).
tff(126,plain,
sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[126,123]) ).
tff(128,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[129,7]) ).
tff(131,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[131,128,115,76,74]) ).
tff(133,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(unit_resolution,[status(thm)],[133,7]) ).
tff(135,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[136,7]) ).
tff(138,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[141,7]) ).
tff(143,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(transitivity,[status(thm)],[143,140]) ).
tff(145,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(transitivity,[status(thm)],[145,135]) ).
tff(147,plain,
( heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,axiom,
heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_6) ).
tff(151,plain,
heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))),
inference(modus_ponens,[status(thm)],[151,148]) ).
tff(153,plain,
( ( x12 = x7 )
<=> ( x7 = x12 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(154,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[154,7]) ).
tff(156,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[157,7]) ).
tff(159,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[161,7]) ).
tff(163,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[163,160]) ).
tff(165,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[166,7]) ).
tff(168,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[168,165,156]) ).
tff(170,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[171,7]) ).
tff(173,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(transitivity,[status(thm)],[173,170]) ).
tff(175,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(unit_resolution,[status(thm)],[176,7]) ).
tff(178,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[179,7]) ).
tff(181,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(182,plain,
sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[181,7]) ).
tff(183,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[184,180]) ).
tff(186,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[189,7]) ).
tff(191,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[184]) ).
tff(192,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[180]) ).
tff(193,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[192,191]) ).
tff(194,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[196,190,188]) ).
tff(198,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(200,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[199,7]) ).
tff(201,plain,
sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[183]) ).
tff(202,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[202,7]) ).
tff(204,plain,
sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[204,201]) ).
tff(206,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[207,7]) ).
tff(209,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[209,206]) ).
tff(211,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[212,7]) ).
tff(214,plain,
sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[214,211]) ).
tff(216,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[216]) ).
tff(219,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[194]) ).
tff(220,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[222,7]) ).
tff(224,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[193]) ).
tff(225,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[226,223,221,218]) ).
tff(228,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[206]) ).
tff(230,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[229,208]) ).
tff(231,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[233,7]) ).
tff(235,plain,
sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[235,232]) ).
tff(237,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[239,7]) ).
tff(241,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[235]) ).
tff(243,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[224]) ).
tff(245,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[232,244]) ).
tff(246,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[245]) ).
tff(247,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(249,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[248,7]) ).
tff(250,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[186]) ).
tff(251,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[252,249,247,243]) ).
tff(254,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(256,plain,
sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(unit_resolution,[status(thm)],[255,7]) ).
tff(257,plain,
sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[260,7]) ).
tff(262,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[262,259]) ).
tff(264,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(266,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[265,7]) ).
tff(267,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[267,264]) ).
tff(269,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[268]) ).
tff(270,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(271,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[270,7]) ).
tff(272,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[272,269]) ).
tff(274,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[273]) ).
tff(275,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(276,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[275,7]) ).
tff(277,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[277,274]) ).
tff(279,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(281,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[280,7]) ).
tff(282,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(transitivity,[status(thm)],[282,279,254,241,238,228,217,200,198]) ).
tff(284,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(transitivity,[status(thm)],[284,178,175]) ).
tff(286,plain,
( heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))),
inference(modus_ponens,[status(thm)],[151,287]) ).
tff(289,plain,
( ( x4 != x7 )
<=> ( x4 != x7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(290,axiom,
x4 != x7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_1) ).
tff(291,plain,
x4 != x7,
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,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(293,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)],[292]) ).
tff(294,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(295,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(296,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)],[295]) ).
tff(297,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(298,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)],[297,296]) ).
tff(299,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)],[298,294]) ).
tff(300,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)],[299]) ).
tff(301,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)],[300,293]) ).
tff(302,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ( x4 = x12 )
| ~ heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ( x4 = x12 )
| ~ heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(303,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ( x4 = x12 )
| ~ heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(304,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ( x4 = x12 )
| ~ heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[303,302]) ).
tff(305,plain,
( ( x4 = x12 )
| ~ heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(unit_resolution,[status(thm)],[304,301,291]) ).
tff(306,plain,
x4 = x12,
inference(unit_resolution,[status(thm)],[305,288]) ).
tff(307,plain,
( ( x4 = x7 )
<=> ( x12 = x7 ) ),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
( ( x4 = x7 )
<=> ( x7 = x12 ) ),
inference(transitivity,[status(thm)],[307,153]) ).
tff(309,plain,
( ( x4 != x7 )
<=> ( x7 != x12 ) ),
inference(monotonicity,[status(thm)],[308]) ).
tff(310,plain,
x7 != x12,
inference(modus_ponens,[status(thm)],[291,309]) ).
tff(311,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x7 = x12 )
| ( x7 = x8 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x7 = x12 )
| ( x7 = x8 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(312,plain,
( ( ( x7 = x8 )
| ( x7 = x12 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ( x7 = x12 )
| ( x7 = x8 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(313,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x7 = x8 )
| ( x7 = x12 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x7 = x12 )
| ( x7 = x8 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(monotonicity,[status(thm)],[312]) ).
tff(314,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x7 = x8 )
| ( x7 = x12 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x7 = x12 )
| ( x7 = x8 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(transitivity,[status(thm)],[313,311]) ).
tff(315,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x7 = x8 )
| ( x7 = x12 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(316,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x7 = x12 )
| ( x7 = x8 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[315,314]) ).
tff(317,plain,
( ( x7 = x12 )
| ( x7 = x8 )
| ~ heap(sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(unit_resolution,[status(thm)],[316,301]) ).
tff(318,plain,
x7 = x8,
inference(unit_resolution,[status(thm)],[317,310,152]) ).
tff(319,plain,
lseg(x4,x7) = lseg(x4,x8),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,plain,
lseg(x4,x8) = lseg(x4,x7),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
x12 = x4,
inference(symmetry,[status(thm)],[306]) ).
tff(322,plain,
lseg(x12,x8) = lseg(x4,x8),
inference(monotonicity,[status(thm)],[321]) ).
tff(323,plain,
lseg(x12,x8) = lseg(x4,x7),
inference(transitivity,[status(thm)],[322,320]) ).
tff(324,plain,
sep(lseg(x12,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[323,132]) ).
tff(325,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[128]) ).
tff(326,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[115]) ).
tff(327,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[76]) ).
tff(328,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[74]) ).
tff(329,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(330,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[329,7]) ).
tff(331,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[89]) ).
tff(333,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(335,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(337,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[336,7]) ).
tff(338,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(transitivity,[status(thm)],[97,100]) ).
tff(339,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[338]) ).
tff(340,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[339]) ).
tff(341,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[341]) ).
tff(343,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[342,337,335,333]) ).
tff(344,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[343]) ).
tff(345,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[344]) ).
tff(346,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(347,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[346,7]) ).
tff(348,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[111]) ).
tff(349,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(351,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[350,7]) ).
tff(352,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[351]) ).
tff(353,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[339]) ).
tff(354,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(356,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[355,7]) ).
tff(357,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[103]) ).
tff(358,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[357]) ).
tff(359,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[358,356,354]) ).
tff(360,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[359]) ).
tff(361,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[361,352,349,347,345]) ).
tff(363,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[362]) ).
tff(364,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(transitivity,[status(thm)],[363,331,328,327,326,325,130]) ).
tff(365,plain,
lseg(x4,x8) = lseg(x12,x8),
inference(symmetry,[status(thm)],[322]) ).
tff(366,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(367,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))),
inference(unit_resolution,[status(thm)],[366,7]) ).
tff(368,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x6,x9),emp)) = sep(lseg(x6,x9),sep(lseg(x4,x7),emp)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(369,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),emp)) = sep(lseg(x6,x9),sep(lseg(x4,x7),emp)),
inference(unit_resolution,[status(thm)],[368,7]) ).
tff(370,plain,
sep(lseg(x6,x9),sep(lseg(x4,x7),emp)) = sep(lseg(x4,x7),sep(lseg(x6,x9),emp)),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))),
inference(monotonicity,[status(thm)],[370]) ).
tff(372,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[371]) ).
tff(373,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(374,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))),
inference(unit_resolution,[status(thm)],[373,7]) ).
tff(375,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))),
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(transitivity,[status(thm)],[375,372]) ).
tff(377,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[376]) ).
tff(378,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))),
inference(symmetry,[status(thm)],[377]) ).
tff(379,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(380,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))),
inference(unit_resolution,[status(thm)],[379,7]) ).
tff(381,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[381]) ).
tff(383,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[382]) ).
tff(384,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[383]) ).
tff(385,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[384]) ).
tff(386,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(387,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[386,7]) ).
tff(388,plain,
sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))),
inference(monotonicity,[status(thm)],[370]) ).
tff(389,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[388]) ).
tff(390,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(391,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))),
inference(unit_resolution,[status(thm)],[390,7]) ).
tff(392,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))),
inference(symmetry,[status(thm)],[391]) ).
tff(393,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))),
inference(symmetry,[status(thm)],[371]) ).
tff(394,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))),
inference(monotonicity,[status(thm)],[393]) ).
tff(395,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[381]) ).
tff(396,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(transitivity,[status(thm)],[395,394,392,389]) ).
tff(397,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[396]) ).
tff(398,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))),
inference(transitivity,[status(thm)],[398,387,385,378,367]) ).
tff(400,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))),
inference(monotonicity,[status(thm)],[399]) ).
tff(401,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[400]) ).
tff(402,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(403,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))),
inference(unit_resolution,[status(thm)],[402,7]) ).
tff(404,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(405,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))),
inference(unit_resolution,[status(thm)],[404,7]) ).
tff(406,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))) = sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))),
inference(symmetry,[status(thm)],[388]) ).
tff(407,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))),
inference(monotonicity,[status(thm)],[406]) ).
tff(408,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))),
inference(transitivity,[status(thm)],[407,405]) ).
tff(409,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))),
inference(monotonicity,[status(thm)],[408]) ).
tff(410,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[410]) ).
tff(412,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))),
inference(symmetry,[status(thm)],[411]) ).
tff(413,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(414,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))),
inference(unit_resolution,[status(thm)],[413,7]) ).
tff(415,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))),
inference(symmetry,[status(thm)],[414]) ).
tff(416,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[417]) ).
tff(419,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[418]) ).
tff(420,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(421,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[420,7]) ).
tff(422,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[415]) ).
tff(423,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[422]) ).
tff(424,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[423]) ).
tff(425,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[424,421,419]) ).
tff(426,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[425]) ).
tff(427,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(429,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[428,7]) ).
tff(430,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[414]) ).
tff(432,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[432]) ).
tff(434,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(435,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[434,7]) ).
tff(436,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[417]) ).
tff(437,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[436,435,433]) ).
tff(438,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[437]) ).
tff(439,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[438]) ).
tff(440,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[439,430,427,412,403,401]) ).
tff(441,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[440]) ).
tff(442,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[441]) ).
tff(443,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(444,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[443,7]) ).
tff(445,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[387]) ).
tff(446,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[377,384,445,397]) ).
tff(447,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[446]) ).
tff(448,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(449,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))),
inference(unit_resolution,[status(thm)],[448,7]) ).
tff(450,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[376]) ).
tff(451,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))),
inference(symmetry,[status(thm)],[450]) ).
tff(452,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))),
inference(monotonicity,[status(thm)],[451]) ).
tff(453,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[452,449,447]) ).
tff(454,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[453]) ).
tff(455,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(456,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[455,7]) ).
tff(457,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[456]) ).
tff(458,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))),
inference(monotonicity,[status(thm)],[451]) ).
tff(459,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[458]) ).
tff(460,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(461,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))),
inference(unit_resolution,[status(thm)],[460,7]) ).
tff(462,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))),
inference(symmetry,[status(thm)],[461]) ).
tff(463,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[376]) ).
tff(464,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[463]) ).
tff(465,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),emp)))))),
inference(symmetry,[status(thm)],[464]) ).
tff(466,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[465,462,459]) ).
tff(467,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[466]) ).
tff(468,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[467,457,454,444,442]) ).
tff(469,plain,
x8 = x7,
inference(symmetry,[status(thm)],[318]) ).
tff(470,plain,
lseg(x3,x8) = lseg(x3,x7),
inference(monotonicity,[status(thm)],[469]) ).
tff(471,plain,
sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[470,468]) ).
tff(472,plain,
( heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ),
inference(monotonicity,[status(thm)],[471]) ).
tff(473,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))
<=> heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ),
inference(symmetry,[status(thm)],[472]) ).
tff(474,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[363]) ).
tff(475,plain,
sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[78]) ).
tff(476,plain,
sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[475,81]) ).
tff(477,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[476]) ).
tff(478,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(479,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[478,7]) ).
tff(480,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[479]) ).
tff(481,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[480,477]) ).
tff(482,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[481]) ).
tff(483,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(484,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[483,7]) ).
tff(485,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[484]) ).
tff(486,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[485,482]) ).
tff(487,plain,
sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[486]) ).
tff(488,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(489,plain,
sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[488,7]) ).
tff(490,plain,
sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[489]) ).
tff(491,plain,
sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[490,487]) ).
tff(492,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[491]) ).
tff(493,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(494,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[493,7]) ).
tff(495,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[494]) ).
tff(496,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[444]) ).
tff(497,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[441,496]) ).
tff(498,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[169]) ).
tff(499,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(500,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[499,7]) ).
tff(501,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[500]) ).
tff(502,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[206]) ).
tff(503,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(504,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[503,7]) ).
tff(505,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[504]) ).
tff(506,plain,
sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[204]) ).
tff(507,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[506]) ).
tff(508,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[507]) ).
tff(509,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[508,505,502]) ).
tff(510,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[509]) ).
tff(511,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(512,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[511,7]) ).
tff(513,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[512]) ).
tff(514,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(515,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[514,7]) ).
tff(516,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[515]) ).
tff(517,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x6,x7),sep(lseg(x8,x11),emp)) = sep(lseg(x8,x11),sep(lseg(x6,x7),emp)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(518,plain,
sep(lseg(x6,x7),sep(lseg(x8,x11),emp)) = sep(lseg(x8,x11),sep(lseg(x6,x7),emp)),
inference(unit_resolution,[status(thm)],[517,7]) ).
tff(519,plain,
sep(lseg(x8,x11),sep(lseg(x6,x7),emp)) = sep(lseg(x6,x7),sep(lseg(x8,x11),emp)),
inference(symmetry,[status(thm)],[518]) ).
tff(520,plain,
sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))) = sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))),
inference(monotonicity,[status(thm)],[519]) ).
tff(521,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))) = sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[520]) ).
tff(522,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))) = sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(523,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))) = sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))),
inference(unit_resolution,[status(thm)],[522,7]) ).
tff(524,plain,
sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))) = sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))),
inference(symmetry,[status(thm)],[523]) ).
tff(525,plain,
sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))) = sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[524,521]) ).
tff(526,plain,
sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))))) = sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[525]) ).
tff(527,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))))) = sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(528,plain,
sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))))) = sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))))),
inference(unit_resolution,[status(thm)],[527,7]) ).
tff(529,plain,
sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))))) = sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))))),
inference(symmetry,[status(thm)],[528]) ).
tff(530,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))) = sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(531,plain,
sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))) = sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))),
inference(unit_resolution,[status(thm)],[530,7]) ).
tff(532,plain,
sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))) = sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))),
inference(monotonicity,[status(thm)],[519]) ).
tff(533,plain,
sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))),
inference(symmetry,[status(thm)],[532]) ).
tff(534,plain,
sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))),
inference(monotonicity,[status(thm)],[533]) ).
tff(535,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))) = sep(lseg(x8,x11),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(536,plain,
sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))) = sep(lseg(x8,x11),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))),
inference(unit_resolution,[status(thm)],[535,7]) ).
tff(537,plain,
sep(lseg(x8,x11),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))) = sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))),
inference(symmetry,[status(thm)],[536]) ).
tff(538,plain,
sep(lseg(x8,x11),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))) = sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))),
inference(transitivity,[status(thm)],[537,532]) ).
tff(539,plain,
sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))) = sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[538]) ).
tff(540,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(541,plain,
sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))),
inference(unit_resolution,[status(thm)],[540,7]) ).
tff(542,plain,
sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))) = sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))),
inference(symmetry,[status(thm)],[541]) ).
tff(543,plain,
sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))) = sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp)))),
inference(transitivity,[status(thm)],[542,539,534,531]) ).
tff(544,plain,
sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))) = sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))))),
inference(monotonicity,[status(thm)],[543]) ).
tff(545,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))) = sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(546,plain,
sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))) = sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))),
inference(unit_resolution,[status(thm)],[545,7]) ).
tff(547,plain,
sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))) = sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))),
inference(symmetry,[status(thm)],[546]) ).
tff(548,plain,
sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))) = sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[547,544,529,526]) ).
tff(549,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[548]) ).
tff(550,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(551,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))),
inference(unit_resolution,[status(thm)],[550,7]) ).
tff(552,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[552,549]) ).
tff(554,plain,
sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[553]) ).
tff(555,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))) = sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(556,plain,
sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))) = sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))),
inference(unit_resolution,[status(thm)],[555,7]) ).
tff(557,plain,
sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))) = sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))),
inference(symmetry,[status(thm)],[556]) ).
tff(558,plain,
sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[557,554,516]) ).
tff(559,plain,
sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[558]) ).
tff(560,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(561,plain,
sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[560,7]) ).
tff(562,plain,
sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))),
inference(symmetry,[status(thm)],[561]) ).
tff(563,plain,
sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[562,559]) ).
tff(564,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[563]) ).
tff(565,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(566,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[565,7]) ).
tff(567,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))),
inference(symmetry,[status(thm)],[566]) ).
tff(568,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[567,564,513,510]) ).
tff(569,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[568]) ).
tff(570,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(571,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))),
inference(unit_resolution,[status(thm)],[570,7]) ).
tff(572,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))),
inference(symmetry,[status(thm)],[571]) ).
tff(573,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(transitivity,[status(thm)],[572,569,501,498]) ).
tff(574,plain,
lseg(x8,x12) = lseg(x7,x12),
inference(monotonicity,[status(thm)],[469]) ).
tff(575,plain,
sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(monotonicity,[status(thm)],[574,573]) ).
tff(576,plain,
sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(transitivity,[status(thm)],[575,135]) ).
tff(577,plain,
( heap(sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp))))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[576]) ).
tff(578,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))))) ),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
heap(sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))))),
inference(modus_ponens,[status(thm)],[151,578]) ).
tff(580,plain,
( ( x8 = x12 )
<=> ( x7 = x12 ) ),
inference(monotonicity,[status(thm)],[469]) ).
tff(581,plain,
( ( x7 = x12 )
<=> ( x8 = x12 ) ),
inference(symmetry,[status(thm)],[580]) ).
tff(582,plain,
( ( x7 != x12 )
<=> ( x8 != x12 ) ),
inference(monotonicity,[status(thm)],[581]) ).
tff(583,plain,
x8 != x12,
inference(modus_ponens,[status(thm)],[310,582]) ).
tff(584,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x8 = x11 )
| ( x8 = x12 )
| ~ heap(sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x8 = x11 )
| ( x8 = x12 )
| ~ heap(sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(585,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x8 = x11 )
| ( x8 = x12 )
| ~ heap(sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(586,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x8 = x11 )
| ( x8 = x12 )
| ~ heap(sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[585,584]) ).
tff(587,plain,
( ( x8 = x11 )
| ( x8 = x12 )
| ~ heap(sep(lseg(x8,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),emp)))))))))))) ),
inference(unit_resolution,[status(thm)],[586,301]) ).
tff(588,plain,
x8 = x11,
inference(unit_resolution,[status(thm)],[587,583,579]) ).
tff(589,plain,
x11 = x8,
inference(symmetry,[status(thm)],[588]) ).
tff(590,plain,
lseg(x8,x11) = lseg(x7,x8),
inference(monotonicity,[status(thm)],[469,589]) ).
tff(591,plain,
lseg(x7,x8) = lseg(x8,x11),
inference(symmetry,[status(thm)],[590]) ).
tff(592,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[591,497]) ).
tff(593,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(594,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[593,7]) ).
tff(595,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[594]) ).
tff(596,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(transitivity,[status(thm)],[595,432]) ).
tff(597,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[596]) ).
tff(598,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[597]) ).
tff(599,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(600,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[599,7]) ).
tff(601,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[596]) ).
tff(602,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[601]) ).
tff(603,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[602]) ).
tff(604,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[603,600,598]) ).
tff(605,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[604]) ).
tff(606,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[605]) ).
tff(607,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(608,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[607,7]) ).
tff(609,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[608]) ).
tff(610,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[596]) ).
tff(611,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[610]) ).
tff(612,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(613,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[612,7]) ).
tff(614,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[613]) ).
tff(615,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[597]) ).
tff(616,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[615]) ).
tff(617,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[616,614,611]) ).
tff(618,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[617]) ).
tff(619,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[618]) ).
tff(620,plain,
lseg(x8,x8) = lseg(x7,x8),
inference(monotonicity,[status(thm)],[469]) ).
tff(621,plain,
sep(lseg(x8,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[620]) ).
tff(622,plain,
^ [Sigma: $i,X: $i] :
refl(( ( sep(lseg(X,X),Sigma) = Sigma )
<=> ( sep(lseg(X,X),Sigma) = Sigma ) )),
inference(bind,[status(th)],[]) ).
tff(623,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)],[622]) ).
tff(624,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(625,axiom,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',normalization) ).
tff(626,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[625,624]) ).
tff(627,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(skolemize,[status(sab)],[626]) ).
tff(628,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[627,623]) ).
tff(629,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x8,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(630,plain,
sep(lseg(x8,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[629,628]) ).
tff(631,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[630]) ).
tff(632,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[631,621,619,609,606,444,442]) ).
tff(633,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[632]) ).
tff(634,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[441,496,605,608,618,633,592,495,492,330,474]) ).
tff(635,plain,
sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[634]) ).
tff(636,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) ),
inference(monotonicity,[status(thm)],[635]) ).
tff(637,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ),
inference(symmetry,[status(thm)],[636]) ).
tff(638,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[495,492,330,474]) ).
tff(639,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(640,plain,
sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))),
inference(unit_resolution,[status(thm)],[639,7]) ).
tff(641,plain,
sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))),
inference(symmetry,[status(thm)],[640]) ).
tff(642,plain,
sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[641]) ).
tff(643,plain,
sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[642]) ).
tff(644,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(645,plain,
sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[644,7]) ).
tff(646,plain,
sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[645]) ).
tff(647,plain,
sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[646,643]) ).
tff(648,plain,
sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[647]) ).
tff(649,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(650,plain,
sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[649,7]) ).
tff(651,plain,
sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[650]) ).
tff(652,plain,
sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[651,648]) ).
tff(653,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[652]) ).
tff(654,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(655,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[654,7]) ).
tff(656,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[655]) ).
tff(657,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[656,653]) ).
tff(658,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[657]) ).
tff(659,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(660,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[659,7]) ).
tff(661,plain,
sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[660]) ).
tff(662,plain,
sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[661,658]) ).
tff(663,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[662]) ).
tff(664,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[663]) ).
tff(665,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[648]) ).
tff(666,plain,
sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[256]) ).
tff(667,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[666]) ).
tff(668,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[667]) ).
tff(669,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(670,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[669,7]) ).
tff(671,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[670]) ).
tff(672,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[671,668,665,650]) ).
tff(673,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[672]) ).
tff(674,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[673]) ).
tff(675,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[674]) ).
tff(676,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[675]) ).
tff(677,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(678,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[677,7]) ).
tff(679,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[671,668]) ).
tff(680,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[679]) ).
tff(681,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[680]) ).
tff(682,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[681]) ).
tff(683,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[682,678,676]) ).
tff(684,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[683]) ).
tff(685,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[684]) ).
tff(686,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(687,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[686,7]) ).
tff(688,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[679]) ).
tff(689,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[688]) ).
tff(690,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(691,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[690,7]) ).
tff(692,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[691]) ).
tff(693,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[674]) ).
tff(694,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[693,692,689]) ).
tff(695,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[694]) ).
tff(696,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[695]) ).
tff(697,plain,
sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[666]) ).
tff(698,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(699,plain,
sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[698,7]) ).
tff(700,plain,
sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[699]) ).
tff(701,plain,
sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[700,697]) ).
tff(702,plain,
sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[701]) ).
tff(703,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[702]) ).
tff(704,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[703]) ).
tff(705,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[704]) ).
tff(706,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(707,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[706,7]) ).
tff(708,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[707]) ).
tff(709,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[708,705]) ).
tff(710,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[709]) ).
tff(711,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[710]) ).
tff(712,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[711]) ).
tff(713,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[712]) ).
tff(714,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(715,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[714,7]) ).
tff(716,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[715]) ).
tff(717,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[680]) ).
tff(718,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[717]) ).
tff(719,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[718]) ).
tff(720,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(721,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[720,7]) ).
tff(722,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[688]) ).
tff(723,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[722]) ).
tff(724,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[704,707]) ).
tff(725,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[724]) ).
tff(726,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[726,723,721,719]) ).
tff(728,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[727]) ).
tff(729,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[728]) ).
tff(730,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(731,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[730,7]) ).
tff(732,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[721]) ).
tff(733,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[718,732,722,725,731]) ).
tff(734,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[733]) ).
tff(735,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[734]) ).
tff(736,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(737,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[736,7]) ).
tff(738,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[737]) ).
tff(739,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))) = sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(740,plain,
sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))) = sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))),
inference(unit_resolution,[status(thm)],[739,7]) ).
tff(741,plain,
sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))),
inference(symmetry,[status(thm)],[520]) ).
tff(742,plain,
sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) = sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))),
inference(transitivity,[status(thm)],[641,741,740]) ).
tff(743,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))),
inference(monotonicity,[status(thm)],[742]) ).
tff(744,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[743]) ).
tff(745,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(746,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))),
inference(unit_resolution,[status(thm)],[745,7]) ).
tff(747,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))),
inference(symmetry,[status(thm)],[746]) ).
tff(748,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[747,744]) ).
tff(749,plain,
sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[748]) ).
tff(750,plain,
sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[749,646,643,666,699]) ).
tff(751,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[750]) ).
tff(752,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(753,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))),
inference(unit_resolution,[status(thm)],[752,7]) ).
tff(754,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))),
inference(symmetry,[status(thm)],[753]) ).
tff(755,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[754,751]) ).
tff(756,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[755]) ).
tff(757,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(758,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(unit_resolution,[status(thm)],[757,7]) ).
tff(759,plain,
sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(symmetry,[status(thm)],[758]) ).
tff(760,plain,
sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[759,756]) ).
tff(761,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[760]) ).
tff(762,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(symmetry,[status(thm)],[761]) ).
tff(763,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(764,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[763,7]) ).
tff(765,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[764]) ).
tff(766,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[765]) ).
tff(767,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(transitivity,[status(thm)],[766,762]) ).
tff(768,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))),
inference(monotonicity,[status(thm)],[767]) ).
tff(769,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[768]) ).
tff(770,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(771,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[770,7]) ).
tff(772,plain,
sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(symmetry,[status(thm)],[771]) ).
tff(773,plain,
sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))),
inference(monotonicity,[status(thm)],[772]) ).
tff(774,plain,
sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[773,769,738,735,729,716,713,696,687,685,664]) ).
tff(775,plain,
sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[470,774]) ).
tff(776,plain,
( heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(monotonicity,[status(thm)],[775]) ).
tff(777,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
<=> heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ),
inference(symmetry,[status(thm)],[776]) ).
tff(778,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(779,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(unit_resolution,[status(thm)],[778,7]) ).
tff(780,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(symmetry,[status(thm)],[779]) ).
tff(781,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(782,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[781,7]) ).
tff(783,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[137]) ).
tff(784,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[783]) ).
tff(785,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[783]) ).
tff(786,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(787,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[786,7]) ).
tff(788,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[787]) ).
tff(789,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[788,785]) ).
tff(790,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[789]) ).
tff(791,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(792,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[791,7]) ).
tff(793,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[792]) ).
tff(794,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(transitivity,[status(thm)],[793,790,784,782]) ).
tff(795,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(monotonicity,[status(thm)],[794]) ).
tff(796,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(797,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(unit_resolution,[status(thm)],[796,7]) ).
tff(798,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(symmetry,[status(thm)],[797]) ).
tff(799,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(800,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[799,7]) ).
tff(801,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[800]) ).
tff(802,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[801]) ).
tff(803,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[802]) ).
tff(804,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(805,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[804,7]) ).
tff(806,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[805]) ).
tff(807,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[806,803]) ).
tff(808,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[807]) ).
tff(809,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[808]) ).
tff(810,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[809]) ).
tff(811,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[810]) ).
tff(812,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(813,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[812,7]) ).
tff(814,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[813]) ).
tff(815,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[801]) ).
tff(816,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(817,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[816,7]) ).
tff(818,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[817]) ).
tff(819,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[818,815]) ).
tff(820,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[819]) ).
tff(821,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[820]) ).
tff(822,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(823,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[822,7]) ).
tff(824,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[819]) ).
tff(825,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[824]) ).
tff(826,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[825]) ).
tff(827,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[807]) ).
tff(828,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[827,826,823,821]) ).
tff(829,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[828]) ).
tff(830,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[829]) ).
tff(831,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(832,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[831,7]) ).
tff(833,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[832]) ).
tff(834,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[833,820]) ).
tff(835,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[834]) ).
tff(836,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(837,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[836,7]) ).
tff(838,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[837]) ).
tff(839,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[838,835]) ).
tff(840,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[839]) ).
tff(841,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(842,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[841,7]) ).
tff(843,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[842]) ).
tff(844,plain,
lseg(x12,x7) = lseg(x4,x7),
inference(monotonicity,[status(thm)],[321]) ).
tff(845,plain,
sep(lseg(x12,x7),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[844]) ).
tff(846,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[687]) ).
tff(847,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[663,684,846,695,712,715,728]) ).
tff(848,plain,
sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x12,x7),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[847]) ).
tff(849,plain,
sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(transitivity,[status(thm)],[848,845,843,840,830,814,811]) ).
tff(850,plain,
sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(monotonicity,[status(thm)],[849]) ).
tff(851,plain,
sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(transitivity,[status(thm)],[850,798,795,780,145,135]) ).
tff(852,plain,
( heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[851]) ).
tff(853,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ),
inference(symmetry,[status(thm)],[852]) ).
tff(854,plain,
heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))),
inference(modus_ponens,[status(thm)],[151,853]) ).
tff(855,plain,
^ [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
<=> ( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) )),
inference(bind,[status(th)],[]) ).
tff(856,plain,
( ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
<=> ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) ),
inference(quant_intro,[status(thm)],[855]) ).
tff(857,plain,
( ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
<=> ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(858,plain,
^ [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma))))
| ( Z = W )
| heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma))) )
<=> ( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) )),
inference(bind,[status(th)],[]) ).
tff(859,plain,
( ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma))))
| ( Z = W )
| heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma))) )
<=> ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ) ),
inference(quant_intro,[status(thm)],[858]) ).
tff(860,axiom,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma))))
| ( Z = W )
| heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',unfolding_5) ).
tff(861,plain,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ),
inference(modus_ponens,[status(thm)],[860,859]) ).
tff(862,plain,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ),
inference(modus_ponens,[status(thm)],[861,857]) ).
tff(863,plain,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ),
inference(skolemize,[status(sab)],[862]) ).
tff(864,plain,
! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) ),
inference(modus_ponens,[status(thm)],[863,856]) ).
tff(865,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(866,plain,
( ( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ( x7 = x12 )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(867,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(monotonicity,[status(thm)],[866]) ).
tff(868,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(transitivity,[status(thm)],[867,865]) ).
tff(869,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(870,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[869,868]) ).
tff(871,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ),
inference(unit_resolution,[status(thm)],[870,864,310]) ).
tff(872,plain,
heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))),
inference(unit_resolution,[status(thm)],[871,854]) ).
tff(873,plain,
heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))),
inference(modus_ponens,[status(thm)],[872,777]) ).
tff(874,plain,
( ( x3 != x8 )
<=> ( x3 != x8 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(875,axiom,
x3 != x8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_3) ).
tff(876,plain,
x3 != x8,
inference(modus_ponens,[status(thm)],[875,874]) ).
tff(877,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(878,plain,
( ( ( x3 = x5 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) )
<=> ( ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(879,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x5 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ) ),
inference(monotonicity,[status(thm)],[878]) ).
tff(880,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x5 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ) ),
inference(transitivity,[status(thm)],[879,877]) ).
tff(881,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x5 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(882,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[881,880]) ).
tff(883,plain,
( ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ),
inference(unit_resolution,[status(thm)],[882,301,876]) ).
tff(884,plain,
x3 = x5,
inference(unit_resolution,[status(thm)],[883,873]) ).
tff(885,plain,
lseg(x3,x7) = lseg(x5,x8),
inference(monotonicity,[status(thm)],[884,318]) ).
tff(886,plain,
lseg(x5,x8) = lseg(x3,x7),
inference(symmetry,[status(thm)],[885]) ).
tff(887,plain,
sep(lseg(x5,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[886,638]) ).
tff(888,plain,
( heap(sep(lseg(x5,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) ),
inference(monotonicity,[status(thm)],[887]) ).
tff(889,plain,
( heap(sep(lseg(x5,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))))
<=> heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ),
inference(transitivity,[status(thm)],[888,637,473]) ).
tff(890,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[492]) ).
tff(891,plain,
sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[574]) ).
tff(892,plain,
sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(transitivity,[status(thm)],[891,363,331,890,494]) ).
tff(893,plain,
sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(monotonicity,[status(thm)],[892]) ).
tff(894,plain,
( heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x5,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))) ),
inference(monotonicity,[status(thm)],[893]) ).
tff(895,plain,
lseg(x1,x8) = lseg(x1,x7),
inference(monotonicity,[status(thm)],[469]) ).
tff(896,plain,
sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[895,638]) ).
tff(897,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(symmetry,[status(thm)],[896]) ).
tff(898,plain,
sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[895,891]) ).
tff(899,plain,
sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(transitivity,[status(thm)],[898,897]) ).
tff(900,plain,
sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))),
inference(monotonicity,[status(thm)],[899]) ).
tff(901,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))))) ),
inference(monotonicity,[status(thm)],[900]) ).
tff(902,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(symmetry,[status(thm)],[901]) ).
tff(903,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(904,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[903,7]) ).
tff(905,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[904]) ).
tff(906,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[362]) ).
tff(907,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(908,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[907,7]) ).
tff(909,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[476]) ).
tff(910,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[909]) ).
tff(911,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[910,908]) ).
tff(912,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[911]) ).
tff(913,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[912]) ).
tff(914,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(915,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[914,7]) ).
tff(916,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[915]) ).
tff(917,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[916,913]) ).
tff(918,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[917]) ).
tff(919,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[918,351,360]) ).
tff(920,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[919]) ).
tff(921,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(922,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[921,7]) ).
tff(923,plain,
sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[917]) ).
tff(924,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[923]) ).
tff(925,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[924]) ).
tff(926,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[925,922,920,906,905]) ).
tff(927,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[926]) ).
tff(928,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(929,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[928,7]) ).
tff(930,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(931,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[930,7]) ).
tff(932,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[931]) ).
tff(933,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[103]) ).
tff(934,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[933]) ).
tff(935,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[934]) ).
tff(936,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(937,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[936,7]) ).
tff(938,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[937]) ).
tff(939,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[938,935]) ).
tff(940,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[939]) ).
tff(941,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(942,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[941,7]) ).
tff(943,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[942]) ).
tff(944,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[943,940,932]) ).
tff(945,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[944]) ).
tff(946,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(947,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[946,7]) ).
tff(948,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(949,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[948,7]) ).
tff(950,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[108]) ).
tff(951,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[950,949]) ).
tff(952,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[951]) ).
tff(953,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[952]) ).
tff(954,plain,
sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[89]) ).
tff(955,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[954]) ).
tff(956,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(957,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[956,7]) ).
tff(958,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[957]) ).
tff(959,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[91]) ).
tff(960,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[959,958,955]) ).
tff(961,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[960]) ).
tff(962,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(963,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[962,7]) ).
tff(964,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[963]) ).
tff(965,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[114]) ).
tff(966,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[965,964,961,953,947,945]) ).
tff(967,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[966]) ).
tff(968,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(969,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[968,7]) ).
tff(970,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[969]) ).
tff(971,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[328,327,326]) ).
tff(972,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[971]) ).
tff(973,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[972,970,967,929,927]) ).
tff(974,plain,
sep(lseg(x1,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[973]) ).
tff(975,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(976,plain,
sep(lseg(x1,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[975,7]) ).
tff(977,plain,
sep(lseg(x5,x1),sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x1,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[976]) ).
tff(978,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[330,474]) ).
tff(979,plain,
sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[978]) ).
tff(980,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[979]) ).
tff(981,plain,
sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[896,980]) ).
tff(982,plain,
sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[981]) ).
tff(983,plain,
sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))) = sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(transitivity,[status(thm)],[982,977,974]) ).
tff(984,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))))
<=> heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(monotonicity,[status(thm)],[983]) ).
tff(985,plain,
( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))))) ),
inference(symmetry,[status(thm)],[984]) ).
tff(986,plain,
( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(transitivity,[status(thm)],[985,902]) ).
tff(987,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[158]) ).
tff(988,plain,
sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[205]) ).
tff(989,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(990,plain,
sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[989,7]) ).
tff(991,plain,
sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[990]) ).
tff(992,plain,
sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[991,988,987]) ).
tff(993,plain,
sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[992]) ).
tff(994,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(995,plain,
sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[994,7]) ).
tff(996,plain,
sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[995]) ).
tff(997,plain,
sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[996,993,137]) ).
tff(998,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[997]) ).
tff(999,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1000,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[999,7]) ).
tff(1001,plain,
sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1000]) ).
tff(1002,plain,
sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[1001,998]) ).
tff(1003,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[1002]) ).
tff(1004,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1005,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[1004,7]) ).
tff(1006,plain,
sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[1005]) ).
tff(1007,plain,
sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(transitivity,[status(thm)],[1006,1003]) ).
tff(1008,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(monotonicity,[status(thm)],[1007]) ).
tff(1009,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1010,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(unit_resolution,[status(thm)],[1009,7]) ).
tff(1011,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(symmetry,[status(thm)],[1010]) ).
tff(1012,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1013,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[1012,7]) ).
tff(1014,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[640]) ).
tff(1015,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[1014]) ).
tff(1016,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1015,1013]) ).
tff(1017,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1016]) ).
tff(1018,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1017]) ).
tff(1019,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1018]) ).
tff(1020,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1021,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1020,7]) ).
tff(1022,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[1015]) ).
tff(1023,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[1013]) ).
tff(1024,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1023,1022]) ).
tff(1025,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1024]) ).
tff(1026,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1025]) ).
tff(1027,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1026]) ).
tff(1028,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1027,1021,1019]) ).
tff(1029,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1028]) ).
tff(1030,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1021]) ).
tff(1031,plain,
sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[1014]) ).
tff(1032,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1033,plain,
sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(unit_resolution,[status(thm)],[1032,7]) ).
tff(1034,plain,
sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[1033]) ).
tff(1035,plain,
sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[1034,1031]) ).
tff(1036,plain,
sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[1035]) ).
tff(1037,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1036]) ).
tff(1038,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1039,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1038,7]) ).
tff(1040,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1039]) ).
tff(1041,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[1034]) ).
tff(1042,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[1041]) ).
tff(1043,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1042]) ).
tff(1044,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1043,1040,1037]) ).
tff(1045,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1044]) ).
tff(1046,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1047,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1046,7]) ).
tff(1048,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1047]) ).
tff(1049,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1042]) ).
tff(1050,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1049]) ).
tff(1051,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1052,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1051,7]) ).
tff(1053,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1052]) ).
tff(1054,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1053,1050]) ).
tff(1055,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1054]) ).
tff(1056,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1055,1048,1045,1018,1030,1026]) ).
tff(1057,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1056]) ).
tff(1058,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1059,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1058,7]) ).
tff(1060,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1054]) ).
tff(1061,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1060]) ).
tff(1062,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1061]) ).
tff(1063,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1062,1059,1057,1029]) ).
tff(1064,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1063]) ).
tff(1065,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1066,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1065,7]) ).
tff(1067,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1066]) ).
tff(1068,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1067]) ).
tff(1069,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1070,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1069,7]) ).
tff(1071,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1070]) ).
tff(1072,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1073,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1072,7]) ).
tff(1074,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1044]) ).
tff(1075,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1074]) ).
tff(1076,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1075,1073]) ).
tff(1077,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1076]) ).
tff(1078,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1077,1071,1068]) ).
tff(1079,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1078]) ).
tff(1080,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1081,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1080,7]) ).
tff(1082,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1081]) ).
tff(1083,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1017]) ).
tff(1084,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1085,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1084,7]) ).
tff(1086,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1085]) ).
tff(1087,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1086,1083]) ).
tff(1088,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1087]) ).
tff(1089,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1088]) ).
tff(1090,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1089]) ).
tff(1091,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1090]) ).
tff(1092,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1093,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1092,7]) ).
tff(1094,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1093]) ).
tff(1095,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1087]) ).
tff(1096,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1095]) ).
tff(1097,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1096]) ).
tff(1098,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1097,1094,1091]) ).
tff(1099,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1098]) ).
tff(1100,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1101,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1100,7]) ).
tff(1102,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1101]) ).
tff(1103,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1096]) ).
tff(1104,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1103]) ).
tff(1105,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1106,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1105,7]) ).
tff(1107,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1087]) ).
tff(1108,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1107,1018,1030,1026]) ).
tff(1109,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1108]) ).
tff(1110,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1109]) ).
tff(1111,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1028]) ).
tff(1112,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1111]) ).
tff(1113,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1112,1110,1106,1104]) ).
tff(1114,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1113]) ).
tff(1115,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1116,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1115,7]) ).
tff(1117,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1025]) ).
tff(1118,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1117]) ).
tff(1119,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1118]) ).
tff(1120,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1121,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1120,7]) ).
tff(1122,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1121]) ).
tff(1123,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1122,1119]) ).
tff(1124,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1123]) ).
tff(1125,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1124,1116,1111]) ).
tff(1126,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1125]) ).
tff(1127,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1128,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1127,7]) ).
tff(1129,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1123]) ).
tff(1130,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1129]) ).
tff(1131,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1130]) ).
tff(1132,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[1131,1128,1126,1114,1102,1099,1082,1079,1064]) ).
tff(1133,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[1132]) ).
tff(1134,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1135,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[1134,7]) ).
tff(1136,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1117]) ).
tff(1137,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1136]) ).
tff(1138,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1139,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1138,7]) ).
tff(1140,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1139]) ).
tff(1141,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1140,1137]) ).
tff(1142,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1141]) ).
tff(1143,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1142]) ).
tff(1144,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1145,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1144,7]) ).
tff(1146,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1145]) ).
tff(1147,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1146,1143]) ).
tff(1148,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1147]) ).
tff(1149,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1148]) ).
tff(1150,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1151,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1150,7]) ).
tff(1152,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1024]) ).
tff(1153,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1152]) ).
tff(1154,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1155,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1154,7]) ).
tff(1156,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1155]) ).
tff(1157,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1117]) ).
tff(1158,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1157,1156,1153]) ).
tff(1159,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1158]) ).
tff(1160,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1161,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1160,7]) ).
tff(1162,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1161]) ).
tff(1163,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1141]) ).
tff(1164,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1163,1162,1159]) ).
tff(1165,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1164]) ).
tff(1166,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1165]) ).
tff(1167,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[1166,1151,1149]) ).
tff(1168,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[1167]) ).
tff(1169,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1170,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[1169,7]) ).
tff(1171,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[1170]) ).
tff(1172,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1173,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1172,7]) ).
tff(1174,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[1036]) ).
tff(1175,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1174]) ).
tff(1176,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1175,1173]) ).
tff(1177,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1176]) ).
tff(1178,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1177]) ).
tff(1179,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1180,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1179,7]) ).
tff(1181,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1180]) ).
tff(1182,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1181,1178]) ).
tff(1183,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1182]) ).
tff(1184,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1183]) ).
tff(1185,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1184]) ).
tff(1186,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1185]) ).
tff(1187,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1188,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1187,7]) ).
tff(1189,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1188]) ).
tff(1190,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1028]) ).
tff(1191,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1192,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1191,7]) ).
tff(1193,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1157]) ).
tff(1194,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1153]) ).
tff(1195,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1194,1155,1193]) ).
tff(1196,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1195]) ).
tff(1197,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1182]) ).
tff(1198,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1197,1196,1192,1190]) ).
tff(1199,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1198]) ).
tff(1200,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1199]) ).
tff(1201,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1202,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1201,7]) ).
tff(1203,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1042]) ).
tff(1204,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1203]) ).
tff(1205,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1206,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1205,7]) ).
tff(1207,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1206]) ).
tff(1208,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1207,1204]) ).
tff(1209,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1208]) ).
tff(1210,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1209]) ).
tff(1211,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1212,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1211,7]) ).
tff(1213,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1044]) ).
tff(1214,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1213]) ).
tff(1215,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1214,1212,1210,1202]) ).
tff(1216,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1215]) ).
tff(1217,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1216]) ).
tff(1218,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1219,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1218,7]) ).
tff(1220,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1178]) ).
tff(1221,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1220]) ).
tff(1222,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1196]) ).
tff(1223,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1192]) ).
tff(1224,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1190]) ).
tff(1225,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1224,1223,1222,1221,1219,1217]) ).
tff(1226,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1225]) ).
tff(1227,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1226]) ).
tff(1228,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1229,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1228,7]) ).
tff(1230,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[1229,1227,1200,1189,1186]) ).
tff(1231,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[1230]) ).
tff(1232,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x7),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1233,plain,
sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x7),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[1232,7]) ).
tff(1234,plain,
sep(lseg(x6,x7),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[1233]) ).
tff(1235,plain,
sep(lseg(x6,x7),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1234,1036]) ).
tff(1236,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1235]) ).
tff(1237,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1238,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1237,7]) ).
tff(1239,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1238]) ).
tff(1240,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1239,1236]) ).
tff(1241,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1240]) ).
tff(1242,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1243,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1242,7]) ).
tff(1244,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1243]) ).
tff(1245,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1244,1241]) ).
tff(1246,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1245]) ).
tff(1247,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1248,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1247,7]) ).
tff(1249,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1248]) ).
tff(1250,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1249,1246]) ).
tff(1251,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1250]) ).
tff(1252,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1253,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1252,7]) ).
tff(1254,plain,
sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1253]) ).
tff(1255,plain,
sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[1254,1251]) ).
tff(1256,plain,
sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[1255]) ).
tff(1257,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1258,plain,
sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[1257,7]) ).
tff(1259,plain,
sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[1258]) ).
tff(1260,plain,
sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(transitivity,[status(thm)],[1259,1256,1231,1171,1168,1135,1133]) ).
tff(1261,plain,
sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(monotonicity,[status(thm)],[1260]) ).
tff(1262,plain,
sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))),
inference(transitivity,[status(thm)],[1261,1011,1008,780,145,135]) ).
tff(1263,plain,
( heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[1262]) ).
tff(1264,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))))
<=> heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ),
inference(symmetry,[status(thm)],[1263]) ).
tff(1265,plain,
heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))),
inference(modus_ponens,[status(thm)],[151,1264]) ).
tff(1266,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1267,plain,
( ( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ( x7 = x12 )
| heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1268,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(monotonicity,[status(thm)],[1267]) ).
tff(1269,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(transitivity,[status(thm)],[1268,1266]) ).
tff(1270,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1271,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x7 = x12 )
| heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[1270,1269]) ).
tff(1272,plain,
( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ),
inference(unit_resolution,[status(thm)],[1271,864,310]) ).
tff(1273,plain,
heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))),
inference(unit_resolution,[status(thm)],[1272,1265]) ).
tff(1274,plain,
heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))),
inference(modus_ponens,[status(thm)],[1273,986]) ).
tff(1275,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x8 = x12 )
| heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x8 = x12 )
| heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1276,plain,
( ( heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ( x8 = x12 )
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) )
<=> ( ( x8 = x12 )
| heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1277,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ( x8 = x12 )
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x8 = x12 )
| heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(monotonicity,[status(thm)],[1276]) ).
tff(1278,plain,
( ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ( x8 = x12 )
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x8 = x12 )
| heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(transitivity,[status(thm)],[1277,1275]) ).
tff(1279,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ( x8 = x12 )
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1280,plain,
( ~ ! [Sigma: $i,W: $i,Z: $i,Y: $i,X: $i] :
( heap(sep(lseg(X,Z),sep(lseg(Z,W),Sigma)))
| ( Z = W )
| ~ heap(sep(lseg(X,Y),sep(lseg(Y,Z),sep(lseg(Z,W),Sigma)))) )
| ( x8 = x12 )
| heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[1279,1278]) ).
tff(1281,plain,
( heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x5,x1),sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(unit_resolution,[status(thm)],[1280,864,583]) ).
tff(1282,plain,
heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[1281,1274]) ).
tff(1283,plain,
heap(sep(lseg(x5,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))),
inference(modus_ponens,[status(thm)],[1282,894]) ).
tff(1284,plain,
heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(modus_ponens,[status(thm)],[1283,889]) ).
tff(1285,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x12 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x12 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1286,plain,
( ( ( x3 = x12 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) )
<=> ( ( x3 = x8 )
| ( x3 = x12 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1287,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x12 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x12 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ) ),
inference(monotonicity,[status(thm)],[1286]) ).
tff(1288,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x12 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x12 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ) ),
inference(transitivity,[status(thm)],[1287,1285]) ).
tff(1289,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x12 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1290,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x12 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ),
inference(modus_ponens,[status(thm)],[1289,1288]) ).
tff(1291,plain,
( ( x3 = x12 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ),
inference(unit_resolution,[status(thm)],[1290,301,876]) ).
tff(1292,plain,
x3 = x12,
inference(unit_resolution,[status(thm)],[1291,1284]) ).
tff(1293,plain,
x5 = x3,
inference(symmetry,[status(thm)],[884]) ).
tff(1294,plain,
x5 = x4,
inference(transitivity,[status(thm)],[1293,1292,321]) ).
tff(1295,plain,
lseg(x5,x8) = lseg(x4,x8),
inference(monotonicity,[status(thm)],[1294]) ).
tff(1296,plain,
lseg(x3,x7) = lseg(x12,x8),
inference(transitivity,[status(thm)],[885,1295,365]) ).
tff(1297,plain,
sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(monotonicity,[status(thm)],[1296,364]) ).
tff(1298,plain,
sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[1297,324,118]) ).
tff(1299,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) ),
inference(monotonicity,[status(thm)],[1298]) ).
tff(1300,plain,
( heap(sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) ),
inference(symmetry,[status(thm)],[1299]) ).
tff(1301,plain,
( ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
<=> ~ heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) ),
inference(monotonicity,[status(thm)],[1300]) ).
tff(1302,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1303,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1302,7]) ).
tff(1304,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1303]) ).
tff(1305,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1306,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1305,7]) ).
tff(1307,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1306]) ).
tff(1308,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1307]) ).
tff(1309,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1308,37,34,32]) ).
tff(1310,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1309]) ).
tff(1311,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1312,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1311,7]) ).
tff(1313,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1312]) ).
tff(1314,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[1307,51,54]) ).
tff(1315,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1314]) ).
tff(1316,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1315]) ).
tff(1317,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1316]) ).
tff(1318,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1317,1313,1310]) ).
tff(1319,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1318]) ).
tff(1320,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[1317]) ).
tff(1321,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1310]) ).
tff(1322,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[73]) ).
tff(1323,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1324,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1323,7]) ).
tff(1325,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1324]) ).
tff(1326,plain,
lseg(x12,x12) = lseg(x4,x12),
inference(monotonicity,[status(thm)],[321]) ).
tff(1327,plain,
sep(lseg(x12,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1326]) ).
tff(1328,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x12,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1329,plain,
sep(lseg(x12,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1328,628]) ).
tff(1330,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x12,x12),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1329]) ).
tff(1331,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(transitivity,[status(thm)],[1330,1327,1325,1322,1321,1312,1320]) ).
tff(1332,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(monotonicity,[status(thm)],[1331]) ).
tff(1333,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1334,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1333,7]) ).
tff(1335,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1336,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1335,7]) ).
tff(1337,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1336]) ).
tff(1338,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[908]) ).
tff(1339,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1338,909]) ).
tff(1340,plain,
sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1339]) ).
tff(1341,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1342,plain,
sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1341,7]) ).
tff(1343,plain,
sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1342]) ).
tff(1344,plain,
sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1343,1340]) ).
tff(1345,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1344]) ).
tff(1346,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1345,1337,113,96,93]) ).
tff(1347,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1346]) ).
tff(1348,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[1347,1334,1332,1319,1304,118]) ).
tff(1349,plain,
( heap(sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))
<=> heap(sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) ),
inference(monotonicity,[status(thm)],[1348]) ).
tff(1350,plain,
( ~ heap(sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))))
<=> ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) ),
inference(monotonicity,[status(thm)],[1349]) ).
tff(1351,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1345]) ).
tff(1352,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1353,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[1352,7]) ).
tff(1354,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[1353]) ).
tff(1355,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1354,107]) ).
tff(1356,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1355]) ).
tff(1357,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1358,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1357,7]) ).
tff(1359,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1358]) ).
tff(1360,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1359,1356]) ).
tff(1361,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1360]) ).
tff(1362,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1363,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1362,7]) ).
tff(1364,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1363]) ).
tff(1365,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[1364,1361,92,95,112,1336,1351]) ).
tff(1366,plain,
sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[1365]) ).
tff(1367,plain,
( heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))))
<=> heap(sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ),
inference(monotonicity,[status(thm)],[1366]) ).
tff(1368,plain,
( ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))))
<=> ~ heap(sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ),
inference(monotonicity,[status(thm)],[1367]) ).
tff(1369,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1370,plain,
( ( ( x4 = x7 )
| ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) )
<=> ( ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1371,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) ) ),
inference(monotonicity,[status(thm)],[1370]) ).
tff(1372,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) ) ),
inference(transitivity,[status(thm)],[1371,1369]) ).
tff(1373,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1374,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x4 = x7 )
| ~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) ),
inference(modus_ponens,[status(thm)],[1373,1372]) ).
tff(1375,plain,
~ heap(sep(lseg(x4,x7),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))),
inference(unit_resolution,[status(thm)],[1374,301,291]) ).
tff(1376,plain,
~ heap(sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(modus_ponens,[status(thm)],[1375,1368]) ).
tff(1377,plain,
~ heap(sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(modus_ponens,[status(thm)],[1376,1350]) ).
tff(1378,plain,
~ heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(modus_ponens,[status(thm)],[1377,1301]) ).
tff(1379,plain,
heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(modus_ponens,[status(thm)],[1283,888]) ).
tff(1380,plain,
$false,
inference(unit_resolution,[status(thm)],[1379,1378]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW429-1 : TPTP v9.0.0. Released v5.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.34 % Computer : n015.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Fri Jun 20 11:41:40 EDT 2025
% 0.11/0.34 % CPUTime :
% 7.94/8.15 % SZS status Unsatisfiable
% 7.94/8.15 % SZS output start Proof
% See solution above
% 8.38/8.54 % E exiting
%------------------------------------------------------------------------------