TSTP Solution File: SWW429-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW429-1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:58:35 EDT 2022
% Result : Unsatisfiable 5.62s 3.83s
% Output : Proof 6.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 308
% Syntax : Number of formulae : 1795 (1394 unt; 14 typ; 0 def)
% Number of atoms : 2557 (2191 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 1286 ( 516 ~; 662 |; 0 &)
% ( 108 <=>; 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 : 5 ( 3 >; 2 *; 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 : 1166 (1143 !; 0 ?;1166 :)
% 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(x7_type,type,
x7: $i ).
tff(x6_type,type,
x6: $i ).
tff(x9_type,type,
x9: $i ).
tff(x12_type,type,
x12: $i ).
tff(x4_type,type,
x4: $i ).
tff(x1_type,type,
x1: $i ).
tff(x5_type,type,
x5: $i ).
tff(x3_type,type,
x3: $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(x6,x9),sep(lseg(x8,x11),emp)) = sep(lseg(x8,x11),sep(lseg(x6,x9),emp)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
sep(lseg(x6,x9),sep(lseg(x8,x11),emp)) = sep(lseg(x8,x11),sep(lseg(x6,x9),emp)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,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(x8,x11),emp))) = sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))) = sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))),
inference(transitivity,[status(thm)],[13,10]) ).
tff(15,plain,
sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[15]) ).
tff(17,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(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[17,7]) ).
tff(19,plain,
sep(lseg(x8,x11),sep(lseg(x6,x9),emp)) = sep(lseg(x6,x9),sep(lseg(x8,x11),emp)),
inference(symmetry,[status(thm)],[9]) ).
tff(20,plain,
sep(lseg(x6,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))) = sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(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(24,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)],[23,7]) ).
tff(25,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)],[24]) ).
tff(26,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(27,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)],[26,7]) ).
tff(28,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)],[27]) ).
tff(29,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)],[28]) ).
tff(30,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)],[29]) ).
tff(31,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(32,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)],[31,7]) ).
tff(33,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)],[32]) ).
tff(34,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)],[33,30]) ).
tff(35,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)],[34]) ).
tff(36,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(37,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)],[36,7]) ).
tff(38,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)],[37]) ).
tff(39,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(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(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(40,plain,
sep(lseg(x3,x5),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(x3,x5),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)],[39,7]) ).
tff(41,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(42,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)],[41,7]) ).
tff(43,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)],[42]) ).
tff(44,plain,
sep(lseg(x3,x5),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,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)],[43]) ).
tff(45,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,x5),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)],[44]) ).
tff(46,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(x4,x12),sep(lseg(x3,x5),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)],[28,45,40]) ).
tff(47,plain,
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(x4,x12),sep(lseg(x3,x5),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)],[46]) ).
tff(48,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),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(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)],[47]) ).
tff(49,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(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(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(50,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),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(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)],[49,7]) ).
tff(51,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(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)],[50]) ).
tff(52,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(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)],[51,48]) ).
tff(53,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(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)],[52]) ).
tff(54,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(x5,x1),sep(lseg(x3,x5),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(x5,x1),sep(lseg(x3,x5),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(55,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x5,x1),sep(lseg(x3,x5),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)],[54,7]) ).
tff(56,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x5,x1),sep(lseg(x3,x5),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)],[55]) ).
tff(57,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(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)],[56,53]) ).
tff(58,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(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)],[57]) ).
tff(59,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(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(60,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[59,7]) ).
tff(61,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[60]) ).
tff(62,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(63,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)],[62,7]) ).
tff(64,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)],[63]) ).
tff(65,plain,
sep(lseg(x3,x5),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(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,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(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)],[65]) ).
tff(67,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(68,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)],[67,7]) ).
tff(69,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)],[68]) ).
tff(70,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(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[69,66]) ).
tff(71,plain,
sep(lseg(x5,x1),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(x5,x1),sep(lseg(x3,x5),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)],[70]) ).
tff(72,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),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(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[71]) ).
tff(73,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(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(x5,x1),sep(lseg(x7,x12),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(74,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),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(x5,x1),sep(lseg(x7,x12),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)],[73,7]) ).
tff(75,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),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(x7,x12),sep(lseg(x5,x1),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(symmetry,[status(thm)],[74]) ).
tff(76,plain,
sep(lseg(x7,x12),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(x7,x12),sep(lseg(x3,x5),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)],[70]) ).
tff(77,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),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(x3,x5),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)],[76]) ).
tff(78,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),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(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)],[77]) ).
tff(79,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)],[64]) ).
tff(80,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(81,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)],[80,7]) ).
tff(82,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)],[81]) ).
tff(83,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)],[82,79]) ).
tff(84,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(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
sep(lseg(x3,x5),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(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),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(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
sep(lseg(x7,x12),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(x7,x12),sep(lseg(x3,x5),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)],[86]) ).
tff(88,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(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,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(quant_inst,[status(thm)],]) ).
tff(89,plain,
sep(lseg(x7,x12),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,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(unit_resolution,[status(thm)],[88,7]) ).
tff(90,plain,
sep(lseg(x3,x5),sep(lseg(x7,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(x7,x12),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)],[89]) ).
tff(91,plain,
sep(lseg(x3,x5),sep(lseg(x7,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(x7,x12),sep(lseg(x3,x5),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)],[90,87]) ).
tff(92,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),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)],[91]) ).
tff(93,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[92,78,75,72]) ).
tff(94,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[93]) ).
tff(95,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(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(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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(quant_inst,[status(thm)],]) ).
tff(96,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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(unit_resolution,[status(thm)],[95,7]) ).
tff(97,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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)],[96]) ).
tff(98,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),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)],[91]) ).
tff(99,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),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(x7,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)],[98]) ).
tff(100,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x9),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x9),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[100,7]) ).
tff(102,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(103,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)],[102,7]) ).
tff(104,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)],[103]) ).
tff(105,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)],[104]) ).
tff(106,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(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[106,7]) ).
tff(108,plain,
sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))) = 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)],[107]) ).
tff(109,plain,
sep(lseg(x6,x9),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(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[108,105]) ).
tff(110,plain,
sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),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)],[109]) ).
tff(111,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(x6,x9),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,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(x6,x9),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[82,79,111,101]) ).
tff(113,plain,
sep(lseg(x7,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(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,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)],[113]) ).
tff(115,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[115,7]) ).
tff(117,plain,
sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,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(transitivity,[status(thm)],[117,114]) ).
tff(119,plain,
sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,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(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
sep(lseg(x3,x5),sep(lseg(x7,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(x3,x5),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),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(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[86,89,120]) ).
tff(122,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x5),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(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),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(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)],[122]) ).
tff(124,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(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[124,7]) ).
tff(126,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)],[83]) ).
tff(127,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)],[126]) ).
tff(128,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(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(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
sep(lseg(x7,x12),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,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)],[128]) ).
tff(130,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(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(x7,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(quant_inst,[status(thm)],]) ).
tff(131,plain,
sep(lseg(x7,x12),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(x7,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(unit_resolution,[status(thm)],[130,7]) ).
tff(132,plain,
sep(lseg(x7,x8),sep(lseg(x7,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(x7,x12),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)],[131]) ).
tff(133,plain,
sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x7,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(monotonicity,[status(thm)],[118]) ).
tff(134,plain,
sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),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)],[133,132,129]) ).
tff(135,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),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)],[134]) ).
tff(136,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,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,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,x8),sep(lseg(x3,x5),sep(lseg(x7,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(transitivity,[status(thm)],[136,125,123,99]) ).
tff(138,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,x8),sep(lseg(x3,x5),sep(lseg(x7,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(monotonicity,[status(thm)],[137]) ).
tff(139,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)],[105]) ).
tff(140,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(141,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)],[140,7]) ).
tff(142,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)],[141]) ).
tff(143,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)],[142,139]) ).
tff(144,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)],[143]) ).
tff(145,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(146,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)],[145,7]) ).
tff(147,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)],[146]) ).
tff(148,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)],[147,144]) ).
tff(149,plain,
sep(lseg(x7,x12),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,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)],[148]) ).
tff(150,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(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(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(151,plain,
sep(lseg(x7,x12),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(x7,x12),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)],[150,7]) ).
tff(152,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),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(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)],[151]) ).
tff(153,plain,
sep(lseg(x4,x7),sep(lseg(x7,x12),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(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)],[152,149]) ).
tff(154,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),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,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)],[153]) ).
tff(155,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(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,x12),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(156,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x7,x12),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,x12),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)],[155,7]) ).
tff(157,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),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,x12),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)],[156]) ).
tff(158,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),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,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)],[157,154]) ).
tff(159,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),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,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)],[158]) ).
tff(160,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,x12),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,x12),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(161,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),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,x12),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)],[160,7]) ).
tff(162,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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,x12),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)],[161]) ).
tff(163,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[162,159,138,97,94]) ).
tff(164,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[163]) ).
tff(165,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[164,61,58,38,35,25]) ).
tff(166,plain,
( heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[165]) ).
tff(167,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(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[166]) ).
tff(168,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(169,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(170,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)],[169,168]) ).
tff(171,plain,
heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[170,167]) ).
tff(172,plain,
( ( x4 != x7 )
<=> ( x4 != x7 ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,axiom,
x4 != x7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_1) ).
tff(174,plain,
x4 != x7,
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,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(176,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)],[175]) ).
tff(177,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(178,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(179,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)],[178]) ).
tff(180,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(181,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)],[180,179]) ).
tff(182,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)],[181,177]) ).
tff(183,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)],[182]) ).
tff(184,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)],[183,176]) ).
tff(185,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(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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(186,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(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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(187,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(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[186,185]) ).
tff(188,plain,
( ( x4 = x12 )
| ~ heap(sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[187,184,174]) ).
tff(189,plain,
x4 = x12,
inference(unit_resolution,[status(thm)],[188,171]) ).
tff(190,plain,
x12 = x4,
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
lseg(x12,x12) = lseg(x4,x12),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
sep(lseg(x12,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
^ [Sigma: $i,X: $i] :
refl(
( ( sep(lseg(X,X),Sigma) = Sigma )
<=> ( sep(lseg(X,X),Sigma) = Sigma ) )),
inference(bind,[status(th)],]) ).
tff(194,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)],[193]) ).
tff(195,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(196,axiom,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',normalization) ).
tff(197,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(skolemize,[status(sab)],[197]) ).
tff(199,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[198,194]) ).
tff(200,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x12,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(201,plain,
sep(lseg(x12,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))),
inference(unit_resolution,[status(thm)],[200,199]) ).
tff(202,plain,
sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))) = sep(lseg(x12,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,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(204,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)],[203,7]) ).
tff(205,plain,
sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[204,202,192,22,18,16]) ).
tff(206,plain,
( heap(sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))
<=> heap(sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))) ),
inference(monotonicity,[status(thm)],[205]) ).
tff(207,plain,
( heap(sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))
<=> heap(sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) ),
inference(symmetry,[status(thm)],[206]) ).
tff(208,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(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(209,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[208,7]) ).
tff(210,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[211]) ).
tff(213,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),emp))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))),
inference(unit_resolution,[status(thm)],[213,7]) ).
tff(215,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,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(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(218,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[217,7]) ).
tff(219,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(transitivity,[status(thm)],[219,216]) ).
tff(221,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[221,212]) ).
tff(223,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[211]) ).
tff(226,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,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(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[227,7]) ).
tff(229,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[18]) ).
tff(230,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[229,21]) ).
tff(231,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = 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)],[230]) ).
tff(232,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(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(233,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[232,7]) ).
tff(234,plain,
sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = 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)],[234,231]) ).
tff(236,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = 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)],[235]) ).
tff(237,plain,
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(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,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),emp)) = sep(lseg(x6,x7),sep(lseg(x6,x9),emp)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(239,plain,
sep(lseg(x6,x9),sep(lseg(x6,x7),emp)) = sep(lseg(x6,x7),sep(lseg(x6,x9),emp)),
inference(unit_resolution,[status(thm)],[238,7]) ).
tff(240,plain,
sep(lseg(x6,x7),sep(lseg(x6,x9),emp)) = sep(lseg(x6,x9),sep(lseg(x6,x7),emp)),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),emp))) = sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
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),emp))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(246,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[245,7]) ).
tff(247,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))),
inference(transitivity,[status(thm)],[247,244]) ).
tff(249,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(252,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))),
inference(unit_resolution,[status(thm)],[251,7]) ).
tff(253,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(254,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)],[253,7]) ).
tff(255,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(256,plain,
sep(lseg(x6,x7),sep(lseg(x8,x11),emp)) = sep(lseg(x8,x11),sep(lseg(x6,x7),emp)),
inference(unit_resolution,[status(thm)],[255,7]) ).
tff(257,plain,
sep(lseg(x8,x11),sep(lseg(x6,x7),emp)) = sep(lseg(x6,x7),sep(lseg(x8,x11),emp)),
inference(symmetry,[status(thm)],[256]) ).
tff(258,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)],[257]) ).
tff(259,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)],[258]) ).
tff(260,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)],[204]) ).
tff(261,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)],[260,259,254]) ).
tff(262,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)],[261]) ).
tff(263,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)],[262]) ).
tff(264,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(265,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)],[264,7]) ).
tff(266,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)],[265]) ).
tff(267,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)],[266,263]) ).
tff(268,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = 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)],[267]) ).
tff(269,plain,
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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))),
inference(symmetry,[status(thm)],[268]) ).
tff(270,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[269,252,250]) ).
tff(271,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)],[35,25]) ).
tff(272,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)],[271]) ).
tff(273,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)],[272]) ).
tff(274,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)],[170,273]) ).
tff(275,plain,
( ( x12 = x7 )
<=> ( x7 = x12 ) ),
inference(commutativity,[status(thm)],]) ).
tff(276,plain,
( ( x4 = x7 )
<=> ( x12 = x7 ) ),
inference(monotonicity,[status(thm)],[189]) ).
tff(277,plain,
( ( x4 = x7 )
<=> ( x7 = x12 ) ),
inference(transitivity,[status(thm)],[276,275]) ).
tff(278,plain,
( ( x4 != x7 )
<=> ( x7 != x12 ) ),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
x7 != x12,
inference(modus_ponens,[status(thm)],[174,278]) ).
tff(280,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 = 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(rewrite,[status(thm)],]) ).
tff(281,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(282,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(modus_ponens,[status(thm)],[281,280]) ).
tff(283,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)))))))))))) ),
inference(unit_resolution,[status(thm)],[282,184]) ).
tff(284,plain,
x7 = x8,
inference(unit_resolution,[status(thm)],[283,279,274]) ).
tff(285,plain,
x8 = x7,
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
lseg(x8,x8) = lseg(x7,x8),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
lseg(x7,x8) = lseg(x8,x8),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
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(x8,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[287,270]) ).
tff(289,plain,
sep(lseg(x8,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))))) = 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)],[288]) ).
tff(290,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(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(291,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[290,7]) ).
tff(292,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))),
inference(symmetry,[status(thm)],[252]) ).
tff(293,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[249,292,268,291]) ).
tff(294,plain,
sep(lseg(x8,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[293]) ).
tff(295,plain,
sep(lseg(x8,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x8,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x8,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(297,plain,
sep(lseg(x8,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[296,199]) ).
tff(298,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x8,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[297]) ).
tff(299,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)],[103]) ).
tff(300,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)],[299]) ).
tff(301,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(monotonicity,[status(thm)],[300]) ).
tff(302,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(303,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)],[302,7]) ).
tff(304,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)],[303]) ).
tff(305,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)],[304,301]) ).
tff(306,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)],[305]) ).
tff(307,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(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)],[306]) ).
tff(308,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(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(monotonicity,[status(thm)],[307]) ).
tff(309,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(symmetry,[status(thm)],[308]) ).
tff(310,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(311,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)],[310,7]) ).
tff(312,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)],[311]) ).
tff(313,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(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)],[312,309]) ).
tff(314,plain,
sep(lseg(x7,x8),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(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)],[313]) ).
tff(315,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(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)],[314]) ).
tff(316,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(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(317,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[316,7]) ).
tff(318,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)],[260]) ).
tff(319,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(320,plain,
sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(unit_resolution,[status(thm)],[319,7]) ).
tff(321,plain,
sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[320]) ).
tff(322,plain,
sep(lseg(x6,x7),sep(lseg(x1,x6),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(transitivity,[status(thm)],[321,318]) ).
tff(323,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x1,x6),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)],[322]) ).
tff(324,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(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(325,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[324,7]) ).
tff(326,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),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)],[326,323]) ).
tff(328,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),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)],[327]) ).
tff(329,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,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[328]) ).
tff(330,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(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[304,301,329,317]) ).
tff(331,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(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[330]) ).
tff(332,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),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)],[331]) ).
tff(333,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(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(334,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[333,7]) ).
tff(335,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),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(transitivity,[status(thm)],[335,332]) ).
tff(337,plain,
sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),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)],[336]) ).
tff(338,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(x7,x12),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[337]) ).
tff(339,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(x7,x12),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[308,311,338]) ).
tff(340,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(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[339]) ).
tff(341,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),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(symmetry,[status(thm)],[340]) ).
tff(342,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(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(343,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[342,7]) ).
tff(344,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[343]) ).
tff(345,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)],[305]) ).
tff(346,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)],[345]) ).
tff(347,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(monotonicity,[status(thm)],[346]) ).
tff(348,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(symmetry,[status(thm)],[347]) ).
tff(349,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(350,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)],[349,7]) ).
tff(351,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(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)],[350]) ).
tff(352,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(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[331,334]) ).
tff(353,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(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[352]) ).
tff(354,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),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(symmetry,[status(thm)],[353]) ).
tff(355,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),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)],[354,351,348]) ).
tff(356,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),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)],[355]) ).
tff(357,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(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[356]) ).
tff(358,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(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(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(359,plain,
sep(lseg(x5,x1),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(x5,x1),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)],[358,7]) ).
tff(360,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),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(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[360]) ).
tff(362,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[361]) ).
tff(363,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(364,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)],[363,7]) ).
tff(365,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),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(transitivity,[status(thm)],[326,323,299,364]) ).
tff(366,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),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)],[365]) ).
tff(367,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(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(368,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[367,7]) ).
tff(369,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[368]) ).
tff(370,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),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)],[369,366]) ).
tff(371,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),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)],[370]) ).
tff(372,plain,
sep(lseg(x5,x1),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(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[373]) ).
tff(375,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(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(376,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[375,7]) ).
tff(377,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)],[364]) ).
tff(378,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)],[377,300]) ).
tff(379,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)],[378]) ).
tff(380,plain,
sep(lseg(x7,x8),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,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)],[379]) ).
tff(381,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(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(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(382,plain,
sep(lseg(x7,x8),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,x8),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)],[381,7]) ).
tff(383,plain,
sep(lseg(x3,x5),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(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)],[382]) ).
tff(384,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),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)],[370]) ).
tff(385,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),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)],[384,383,380]) ).
tff(386,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),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)],[385]) ).
tff(387,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(x3,x5),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[386]) ).
tff(388,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(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[387,376,374,362]) ).
tff(389,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(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[388]) ).
tff(390,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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(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)],[389]) ).
tff(391,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(x7,x8),sep(lseg(x5,x1),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(x7,x8),sep(lseg(x5,x1),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(392,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x7,x8),sep(lseg(x5,x1),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)],[391,7]) ).
tff(393,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x7,x8),sep(lseg(x5,x1),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)],[392]) ).
tff(394,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x5,x1),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)],[360]) ).
tff(395,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x5,x1),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)],[394]) ).
tff(396,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[395]) ).
tff(397,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),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,x12),sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[372]) ).
tff(398,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[397]) ).
tff(399,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(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(400,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[399,7]) ).
tff(401,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[400]) ).
tff(402,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[401,398]) ).
tff(403,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),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(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[402]) ).
tff(404,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),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(transitivity,[status(thm)],[403,396,393,390,357,344,341,315]) ).
tff(405,plain,
lseg(x3,x8) = lseg(x3,x7),
inference(monotonicity,[status(thm)],[285]) ).
tff(406,plain,
sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x8),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)],[405,404]) ).
tff(407,plain,
( heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x8),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)],[406]) ).
tff(408,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x8),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)))))))))))
<=> heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(symmetry,[status(thm)],[407]) ).
tff(409,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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,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(410,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(x4,x12),sep(lseg(x7,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)],[409,7]) ).
tff(411,plain,
sep(lseg(x4,x12),sep(lseg(x7,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(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)],[410]) ).
tff(412,plain,
sep(lseg(x4,x12),sep(lseg(x7,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(transitivity,[status(thm)],[411,306]) ).
tff(413,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,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)],[412]) ).
tff(414,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(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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(415,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x5),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[414,7]) ).
tff(416,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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(x4,x12),sep(lseg(x7,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)],[415]) ).
tff(417,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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(transitivity,[status(thm)],[416,413]) ).
tff(418,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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(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)],[417]) ).
tff(419,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(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(420,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[419,7]) ).
tff(421,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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)],[420]) ).
tff(422,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(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(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(423,plain,
sep(lseg(x7,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(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[422,7]) ).
tff(424,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[423]) ).
tff(425,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[424]) ).
tff(426,plain,
sep(lseg(x5,x1),sep(lseg(x7,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(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[425]) ).
tff(427,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[426]) ).
tff(428,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x7,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)],[427]) ).
tff(429,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(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(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(430,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[429,7]) ).
tff(431,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[430]) ).
tff(432,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x7,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[431,428]) ).
tff(433,plain,
sep(lseg(x12,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[191,432]) ).
tff(434,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x12,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(435,plain,
sep(lseg(x12,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[434,199]) ).
tff(436,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x12,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[435]) ).
tff(437,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(438,plain,
sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))),
inference(unit_resolution,[status(thm)],[437,7]) ).
tff(439,plain,
sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))) = sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))),
inference(symmetry,[status(thm)],[438]) ).
tff(440,plain,
sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[439]) ).
tff(441,plain,
sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
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(x6,x9),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[441]) ).
tff(443,plain,
sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))) = 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)],[442]) ).
tff(444,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(445,plain,
sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[444,7]) ).
tff(446,plain,
sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[446,443]) ).
tff(448,plain,
sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,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)],[447]) ).
tff(449,plain,
sep(lseg(x7,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(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
sep(lseg(x5,x1),sep(lseg(x7,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(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[449]) ).
tff(451,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,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)],[450]) ).
tff(452,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(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(453,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[452,7]) ).
tff(454,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[453]) ).
tff(455,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[454,451]) ).
tff(456,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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)],[455]) ).
tff(457,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),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(transitivity,[status(thm)],[456,427,430,436,433,421,418,315]) ).
tff(458,plain,
sep(lseg(x3,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x8),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)],[457]) ).
tff(459,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x8),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)],[458]) ).
tff(460,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[456]) ).
tff(461,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[424]) ).
tff(462,plain,
sep(lseg(x7,x8),sep(lseg(x7,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(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[461]) ).
tff(463,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x7,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(x7,x12),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[462]) ).
tff(464,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,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)],[448]) ).
tff(465,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(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(466,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[465,7]) ).
tff(467,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),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)],[447]) ).
tff(469,plain,
sep(lseg(x7,x8),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(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[468]) ).
tff(470,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[469]) ).
tff(471,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(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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(472,plain,
sep(lseg(x7,x8),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(x7,x8),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[471,7]) ).
tff(473,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[472]) ).
tff(474,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[473]) ).
tff(475,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[474,470,467,464]) ).
tff(476,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),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(x7,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)],[475]) ).
tff(477,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,x5),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(478,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[477,7]) ).
tff(479,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[478]) ).
tff(480,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[473]) ).
tff(481,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),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(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[480]) ).
tff(482,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),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(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[481]) ).
tff(483,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[469]) ).
tff(484,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),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)],[483]) ).
tff(485,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(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(486,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[485,7]) ).
tff(487,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[486]) ).
tff(488,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[487,484]) ).
tff(489,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),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)],[488]) ).
tff(490,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[489,482,479,476,463,431,428,460]) ).
tff(491,plain,
sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[490]) ).
tff(492,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))))) ),
inference(monotonicity,[status(thm)],[491]) ).
tff(493,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x8),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(transitivity,[status(thm)],[492,459]) ).
tff(494,plain,
sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[490]) ).
tff(495,plain,
sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[494]) ).
tff(496,plain,
( heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))))))
<=> heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ),
inference(monotonicity,[status(thm)],[495]) ).
tff(497,plain,
( heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))))))
<=> heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ),
inference(symmetry,[status(thm)],[496]) ).
tff(498,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(499,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)],[498,7]) ).
tff(500,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)],[27]) ).
tff(501,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)],[500]) ).
tff(502,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)],[500]) ).
tff(503,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(504,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)],[503,7]) ).
tff(505,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)],[504]) ).
tff(506,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)],[505,502]) ).
tff(507,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)],[506]) ).
tff(508,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(509,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)],[508,7]) ).
tff(510,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)],[509]) ).
tff(511,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)],[510,507,501,499]) ).
tff(512,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)],[511]) ).
tff(513,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(514,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)],[513,7]) ).
tff(515,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)],[514]) ).
tff(516,plain,
sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),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(symmetry,[status(thm)],[63]) ).
tff(517,plain,
sep(lseg(x4,x12),sep(lseg(x1,x6),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(x1,x6),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[516]) ).
tff(518,plain,
sep(lseg(x3,x5),sep(lseg(x4,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(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)],[517]) ).
tff(519,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(x1,x6),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(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(520,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x1,x6),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(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[519,7]) ).
tff(521,plain,
sep(lseg(x4,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(x4,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)],[520]) ).
tff(522,plain,
sep(lseg(x4,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(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)],[521,518]) ).
tff(523,plain,
sep(lseg(x7,x12),sep(lseg(x4,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(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)],[522]) ).
tff(524,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(x1,x6),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(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(525,plain,
sep(lseg(x7,x12),sep(lseg(x4,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(x4,x12),sep(lseg(x7,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)],[524,7]) ).
tff(526,plain,
sep(lseg(x4,x12),sep(lseg(x7,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(x7,x12),sep(lseg(x4,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(symmetry,[status(thm)],[525]) ).
tff(527,plain,
sep(lseg(x4,x12),sep(lseg(x7,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(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)],[526,523]) ).
tff(528,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,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(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)],[527]) ).
tff(529,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(x1,x6),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(x7,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(530,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,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(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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)],[529,7]) ).
tff(531,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,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(symmetry,[status(thm)],[530]) ).
tff(532,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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(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)],[531,528]) ).
tff(533,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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(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)],[532]) ).
tff(534,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(x5,x1),sep(lseg(x7,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(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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(535,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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)],[534,7]) ).
tff(536,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x7,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(symmetry,[status(thm)],[535]) ).
tff(537,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(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(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(538,plain,
sep(lseg(x7,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(x7,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)],[537,7]) ).
tff(539,plain,
sep(lseg(x3,x5),sep(lseg(x7,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,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(symmetry,[status(thm)],[538]) ).
tff(540,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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,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)],[539]) ).
tff(541,plain,
sep(lseg(x5,x1),sep(lseg(x7,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(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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)],[540]) ).
tff(542,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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)],[541]) ).
tff(543,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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(x7,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(symmetry,[status(thm)],[542]) ).
tff(544,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(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(x7,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(545,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,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(x7,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)],[544,7]) ).
tff(546,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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(x7,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)],[545]) ).
tff(547,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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(x7,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(transitivity,[status(thm)],[546,543]) ).
tff(548,plain,
sep(lseg(x12,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x1,x6),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(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[191,547]) ).
tff(549,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x12,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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(x7,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(550,plain,
sep(lseg(x12,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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(x7,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)],[549,199]) ).
tff(551,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x12,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,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)],[550]) ).
tff(552,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x1,x6),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(transitivity,[status(thm)],[105,63]) ).
tff(553,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),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)],[552]) ).
tff(554,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(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(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(555,plain,
sep(lseg(x3,x5),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,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[554,7]) ).
tff(556,plain,
sep(lseg(x4,x7),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,x7),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[555]) ).
tff(557,plain,
sep(lseg(x4,x7),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(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[556,553]) ).
tff(558,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),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(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[557]) ).
tff(559,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(x3,x5),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(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(560,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),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(x3,x5),sep(lseg(x6,x9),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[559,7]) ).
tff(561,plain,
sep(lseg(x4,x7),sep(lseg(x7,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(x4,x7),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)],[560]) ).
tff(562,plain,
sep(lseg(x4,x7),sep(lseg(x7,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(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[561,558]) ).
tff(563,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x7,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(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[562]) ).
tff(564,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(x3,x5),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(x7,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(565,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),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(x7,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)],[564,7]) ).
tff(566,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x7,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(x4,x7),sep(lseg(x7,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)],[565]) ).
tff(567,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x7,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(x1,x6),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[566,563]) ).
tff(568,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x7,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(x7,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)],[567]) ).
tff(569,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(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),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(x5,x1),sep(lseg(x7,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(570,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x5),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(x5,x1),sep(lseg(x7,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)],[569,7]) ).
tff(571,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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(x4,x7),sep(lseg(x5,x1),sep(lseg(x7,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)],[570]) ).
tff(572,plain,
lseg(x12,x7) = lseg(x4,x7),
inference(monotonicity,[status(thm)],[190]) ).
tff(573,plain,
sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,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)],[572,456]) ).
tff(574,plain,
sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),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)],[573,571,568,542,545,551,548,536,533]) ).
tff(575,plain,
sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),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)],[574]) ).
tff(576,plain,
sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),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)],[575,515,512,38,35,25]) ).
tff(577,plain,
( heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),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)],[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(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ),
inference(symmetry,[status(thm)],[577]) ).
tff(579,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ),
inference(transitivity,[status(thm)],[578,497]) ).
tff(580,plain,
heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))),
inference(modus_ponens,[status(thm)],[170,579]) ).
tff(581,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(582,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)],[581]) ).
tff(583,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(584,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(585,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)],[584]) ).
tff(586,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(587,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)],[586,585]) ).
tff(588,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)],[587,583]) ).
tff(589,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)],[588]) ).
tff(590,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)],[589,582]) ).
tff(591,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),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(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(592,plain,
( ( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) )
<=> ( ( x7 = x12 )
| heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(593,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),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(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(monotonicity,[status(thm)],[592]) ).
tff(594,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),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(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(transitivity,[status(thm)],[593,591]) ).
tff(595,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ( x7 = x12 )
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(596,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[595,594]) ).
tff(597,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))
| ~ heap(sep(lseg(x3,x12),sep(lseg(x12,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp))))))))))) ),
inference(unit_resolution,[status(thm)],[596,590,279]) ).
tff(598,plain,
heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x1,x6),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[597,580]) ).
tff(599,plain,
heap(sep(lseg(x3,x7),sep(lseg(x7,x8),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(modus_ponens,[status(thm)],[598,493]) ).
tff(600,plain,
heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))),
inference(modus_ponens,[status(thm)],[599,408]) ).
tff(601,plain,
( ( x3 != x8 )
<=> ( x3 != x8 ) ),
inference(rewrite,[status(thm)],]) ).
tff(602,axiom,
x3 != x8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_3) ).
tff(603,plain,
x3 != x8,
inference(modus_ponens,[status(thm)],[602,601]) ).
tff(604,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(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),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))) )
| ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(605,plain,
( ( ( x3 = x5 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) )
<=> ( ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(606,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(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),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))) )
| ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(monotonicity,[status(thm)],[605]) ).
tff(607,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(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),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))) )
| ( x3 = x8 )
| ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(transitivity,[status(thm)],[606,604]) ).
tff(608,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(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(609,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(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[608,607]) ).
tff(610,plain,
( ( x3 = x5 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(unit_resolution,[status(thm)],[609,184,603]) ).
tff(611,plain,
x3 = x5,
inference(unit_resolution,[status(thm)],[610,600]) ).
tff(612,plain,
x5 = x3,
inference(symmetry,[status(thm)],[611]) ).
tff(613,plain,
lseg(x5,x5) = lseg(x3,x5),
inference(monotonicity,[status(thm)],[612]) ).
tff(614,plain,
sep(lseg(x5,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = 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)],[613,267]) ).
tff(615,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x5,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),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(616,plain,
sep(lseg(x5,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),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)],[615,199]) ).
tff(617,plain,
sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) = sep(lseg(x5,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))),
inference(symmetry,[status(thm)],[616]) ).
tff(618,plain,
sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[15,229,21,262,265,617,614,291,298,295,289,237,228,226,224]) ).
tff(619,plain,
( heap(sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))
<=> heap(sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))) ),
inference(monotonicity,[status(thm)],[618]) ).
tff(620,plain,
( heap(sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))))
<=> heap(sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))) ),
inference(symmetry,[status(thm)],[619]) ).
tff(621,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(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(622,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[621,7]) ).
tff(623,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[211]) ).
tff(624,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[623]) ).
tff(625,plain,
sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[14]) ).
tff(626,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(627,plain,
sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))),
inference(unit_resolution,[status(thm)],[626,7]) ).
tff(628,plain,
sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))) = sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[627]) ).
tff(629,plain,
sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(transitivity,[status(thm)],[628,625]) ).
tff(630,plain,
sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[629]) ).
tff(631,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(632,plain,
sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[631,7]) ).
tff(633,plain,
sep(lseg(x6,x9),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[632]) ).
tff(634,plain,
sep(lseg(x6,x9),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[633,630]) ).
tff(635,plain,
sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[634]) ).
tff(636,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(637,plain,
sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[636,7]) ).
tff(638,plain,
sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[637]) ).
tff(639,plain,
sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[638,635,624,622]) ).
tff(640,plain,
sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[639]) ).
tff(641,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[640]) ).
tff(642,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(643,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[642,7]) ).
tff(644,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[210]) ).
tff(645,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[644,234,231,291]) ).
tff(646,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[645]) ).
tff(647,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(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(648,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[647,7]) ).
tff(649,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[648]) ).
tff(650,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[649,646]) ).
tff(651,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[650]) ).
tff(652,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[651]) ).
tff(653,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,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,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(654,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),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,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[653,7]) ).
tff(655,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),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(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[291]) ).
tff(656,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[655]) ).
tff(657,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[656]) ).
tff(658,plain,
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(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[657]) ).
tff(659,plain,
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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[262,265,617,614,291,298,295,289]) ).
tff(660,plain,
lseg(x8,x12) = lseg(x7,x12),
inference(monotonicity,[status(thm)],[285]) ).
tff(661,plain,
sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x5,x1),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)],[660,360]) ).
tff(662,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),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(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[661]) ).
tff(663,plain,
sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),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(monotonicity,[status(thm)],[370]) ).
tff(664,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,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[663]) ).
tff(665,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(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[664]) ).
tff(666,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(667,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)],[666,7]) ).
tff(668,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)],[667]) ).
tff(669,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)],[668]) ).
tff(670,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(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[669,665,401,398,662]) ).
tff(671,plain,
sep(lseg(x5,x8),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,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[670]) ).
tff(672,plain,
( heap(sep(lseg(x5,x8),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))))))))))
<=> heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[671]) ).
tff(673,plain,
( heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x5,x8),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)],[672]) ).
tff(674,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),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,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[394]) ).
tff(675,plain,
sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x5,x1),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)],[661,674]) ).
tff(676,plain,
lseg(x5,x8) = lseg(x3,x7),
inference(monotonicity,[status(thm)],[612,285]) ).
tff(677,plain,
sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[676,675]) ).
tff(678,plain,
( heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[677]) ).
tff(679,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x5,x8),sep(lseg(x8,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[678]) ).
tff(680,plain,
sep(lseg(x5,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),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(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[613,402]) ).
tff(681,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x5,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(682,plain,
sep(lseg(x5,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[681,199]) ).
tff(683,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x5),sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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(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(transitivity,[status(thm)],[394,397,400,683,680,396,393,390,357,344,341,315]) ).
tff(685,plain,
sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x8),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)],[684]) ).
tff(686,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x8),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)],[685]) ).
tff(687,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x8),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)))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[686]) ).
tff(688,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x8),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)))))))))))
<=> heap(sep(lseg(x5,x8),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(transitivity,[status(thm)],[687,679,673]) ).
tff(689,plain,
heap(sep(lseg(x5,x8),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(modus_ponens,[status(thm)],[599,688]) ).
tff(690,plain,
( ( x5 = x8 )
<=> ( x3 = x8 ) ),
inference(monotonicity,[status(thm)],[612]) ).
tff(691,plain,
( ( x3 = x8 )
<=> ( x5 = x8 ) ),
inference(symmetry,[status(thm)],[690]) ).
tff(692,plain,
( ( x3 != x8 )
<=> ( x5 != x8 ) ),
inference(monotonicity,[status(thm)],[691]) ).
tff(693,plain,
x5 != x8,
inference(modus_ponens,[status(thm)],[603,692]) ).
tff(694,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x1 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),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)))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x1 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),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(rewrite,[status(thm)],]) ).
tff(695,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x1 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),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(696,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x1 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),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(modus_ponens,[status(thm)],[695,694]) ).
tff(697,plain,
( ( x5 = x1 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),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)],[696,184]) ).
tff(698,plain,
x5 = x1,
inference(unit_resolution,[status(thm)],[697,693,689]) ).
tff(699,plain,
x1 = x5,
inference(symmetry,[status(thm)],[698]) ).
tff(700,plain,
lseg(x5,x1) = lseg(x3,x5),
inference(monotonicity,[status(thm)],[612,699]) ).
tff(701,plain,
lseg(x3,x5) = lseg(x5,x1),
inference(symmetry,[status(thm)],[700]) ).
tff(702,plain,
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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[701,659]) ).
tff(703,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[228]) ).
tff(704,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[223,225,703,236,288,294,297,655,702,658,654,652,643,641]) ).
tff(705,plain,
( heap(sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))))
<=> heap(sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))))) ),
inference(monotonicity,[status(thm)],[704]) ).
tff(706,plain,
( heap(sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))))))
<=> heap(sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))) ),
inference(symmetry,[status(thm)],[705]) ).
tff(707,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(708,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[707,7]) ).
tff(709,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))),
inference(transitivity,[status(thm)],[262,265]) ).
tff(710,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = 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)],[709]) ).
tff(711,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(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(712,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[711,7]) ).
tff(713,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),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(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[712]) ).
tff(714,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = 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)],[713,710]) ).
tff(715,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),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)],[714]) ).
tff(716,plain,
sep(lseg(x3,x5),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(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[715]) ).
tff(717,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x3,x5),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(718,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x3,x5),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)],[717,7]) ).
tff(719,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = 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)],[268]) ).
tff(720,plain,
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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))),
inference(symmetry,[status(thm)],[719]) ).
tff(721,plain,
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,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[720,718,716]) ).
tff(722,plain,
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(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[721]) ).
tff(723,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[722]) ).
tff(724,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(x7,x8),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(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(725,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),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(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[724,7]) ).
tff(726,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x8),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(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),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)],[714]) ).
tff(728,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[727]) ).
tff(729,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),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(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x6,x9),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(x5,x1),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(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(731,plain,
sep(lseg(x5,x1),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(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))),
inference(unit_resolution,[status(thm)],[730,7]) ).
tff(732,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x5,x1),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)],[731]) ).
tff(733,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(monotonicity,[status(thm)],[732]) ).
tff(734,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = 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)],[733,729,726,723]) ).
tff(735,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x3,x12),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)],[734]) ).
tff(736,plain,
sep(lseg(x3,x12),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(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(symmetry,[status(thm)],[735]) ).
tff(737,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x5,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(738,plain,
sep(lseg(x5,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))),
inference(unit_resolution,[status(thm)],[737,199]) ).
tff(739,plain,
sep(lseg(x5,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(monotonicity,[status(thm)],[613,732]) ).
tff(740,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x5,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(symmetry,[status(thm)],[739]) ).
tff(741,plain,
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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))),
inference(transitivity,[status(thm)],[722,725,728,740,738,732]) ).
tff(742,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(743,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)],[742,7]) ).
tff(744,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)],[743]) ).
tff(745,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)],[744]) ).
tff(746,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(monotonicity,[status(thm)],[745]) ).
tff(747,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(748,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)],[747,7]) ).
tff(749,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)],[748]) ).
tff(750,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)],[749,746]) ).
tff(751,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)],[750]) ).
tff(752,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),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),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(753,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(x4,x12),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)],[752,7]) ).
tff(754,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = 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(symmetry,[status(thm)],[753]) ).
tff(755,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(756,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)],[755,7]) ).
tff(757,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)],[744]) ).
tff(758,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)],[757]) ).
tff(759,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(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[758]) ).
tff(760,plain,
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,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[759,756]) ).
tff(761,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[760]) ).
tff(762,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)],[19]) ).
tff(763,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)],[762]) ).
tff(764,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)],[763]) ).
tff(765,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)],[764]) ).
tff(766,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(767,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)],[766,7]) ).
tff(768,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)],[767]) ).
tff(769,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)],[768,765]) ).
tff(770,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)],[769]) ).
tff(771,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(monotonicity,[status(thm)],[770]) ).
tff(772,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(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(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(773,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(x7,x8),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)],[772,7]) ).
tff(774,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(symmetry,[status(thm)],[773]) ).
tff(775,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(monotonicity,[status(thm)],[769]) ).
tff(776,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(symmetry,[status(thm)],[775]) ).
tff(777,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(monotonicity,[status(thm)],[776]) ).
tff(778,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[757]) ).
tff(779,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(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[778]) ).
tff(780,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(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(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(782,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)],[781,7]) ).
tff(783,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)],[782]) ).
tff(784,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(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[783,780]) ).
tff(785,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),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(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),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(transitivity,[status(thm)],[785,777,774,771,761,754,751]) ).
tff(787,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),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)],[786]) ).
tff(788,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,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),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(789,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),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)],[788,7]) ).
tff(790,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[789]) ).
tff(791,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),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(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[784]) ).
tff(792,plain,
sep(lseg(x7,x12),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,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[791]) ).
tff(793,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),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(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[792]) ).
tff(794,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),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,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)],[793,790,787]) ).
tff(795,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),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[794]) ).
tff(796,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),sep(lseg(x8,x11),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),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(797,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),sep(lseg(x8,x11),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),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[796,7]) ).
tff(798,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),sep(lseg(x8,x11),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),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[797]) ).
tff(799,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),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),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[775]) ).
tff(800,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(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(801,plain,
sep(lseg(x7,x12),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,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[800,7]) ).
tff(802,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x12),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)],[801]) ).
tff(803,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[768,765,778]) ).
tff(804,plain,
sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[803]) ).
tff(805,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[804]) ).
tff(806,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(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(807,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[806,7]) ).
tff(808,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[807]) ).
tff(809,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[808,805]) ).
tff(810,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[809]) ).
tff(811,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),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(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[810,802,799]) ).
tff(812,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,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(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[811]) ).
tff(813,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(814,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[813,7]) ).
tff(815,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[809]) ).
tff(816,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),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(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[815]) ).
tff(817,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(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(818,plain,
sep(lseg(x7,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(x7,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[817,7]) ).
tff(819,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)],[769]) ).
tff(820,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),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(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[819]) ).
tff(821,plain,
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(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[820]) ).
tff(822,plain,
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(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[821,818,816]) ).
tff(823,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(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[822]) ).
tff(824,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(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[778]) ).
tff(825,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = 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)],[824]) ).
tff(826,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(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(827,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[826,7]) ).
tff(828,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[827]) ).
tff(829,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),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)],[828,825]) ).
tff(830,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),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(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[829]) ).
tff(831,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),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(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[830]) ).
tff(832,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,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(833,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[832,7]) ).
tff(834,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[833]) ).
tff(835,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),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(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[829]) ).
tff(836,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,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[835]) ).
tff(837,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(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[836]) ).
tff(838,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)],[819]) ).
tff(839,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(monotonicity,[status(thm)],[838]) ).
tff(840,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(symmetry,[status(thm)],[839]) ).
tff(841,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(842,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)],[841,7]) ).
tff(843,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(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)],[842]) ).
tff(844,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(x4,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)],[843,840]) ).
tff(845,plain,
sep(lseg(x7,x12),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(x7,x12),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)],[844]) ).
tff(846,plain,
sep(lseg(x7,x12),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(x7,x12),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)],[845,837,834,831,823,814,812]) ).
tff(847,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),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(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),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[846]) ).
tff(848,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x8),sep(lseg(x7,x12),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(x7,x12),sep(lseg(x7,x8),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(849,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),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(x7,x12),sep(lseg(x7,x8),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)],[848,7]) ).
tff(850,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),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(x7,x8),sep(lseg(x7,x12),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(symmetry,[status(thm)],[849]) ).
tff(851,plain,
sep(lseg(x7,x8),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(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(monotonicity,[status(thm)],[844]) ).
tff(852,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(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[851]) ).
tff(853,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(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[836]) ).
tff(854,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,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(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[853]) ).
tff(855,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(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(856,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[855,7]) ).
tff(857,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),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(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[856]) ).
tff(858,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)],[770]) ).
tff(859,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)],[858]) ).
tff(860,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(x3,x5),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)],[859]) ).
tff(861,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(862,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)],[861,7]) ).
tff(863,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(x3,x5),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)],[862]) ).
tff(864,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(x3,x5),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[838]) ).
tff(865,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,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(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[829]) ).
tff(866,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,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(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[865,864,863,860]) ).
tff(867,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,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(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[866]) ).
tff(868,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(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[867]) ).
tff(869,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,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(870,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[869,7]) ).
tff(871,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)],[756]) ).
tff(872,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(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[871,758]) ).
tff(873,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,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(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[872]) ).
tff(874,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[873]) ).
tff(875,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,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[874,870]) ).
tff(876,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(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[875]) ).
tff(877,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,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(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[876]) ).
tff(878,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(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(879,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[878,7]) ).
tff(880,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),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)],[750]) ).
tff(881,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(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(882,plain,
sep(lseg(x3,x5),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(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[881,7]) ).
tff(883,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),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)],[882]) ).
tff(884,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),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)],[883,880]) ).
tff(885,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[884]) ).
tff(886,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),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(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[885]) ).
tff(887,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),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,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[886,879,877,868,857,854,852]) ).
tff(888,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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(x7,x8),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)],[887]) ).
tff(889,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),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(transitivity,[status(thm)],[888,850,847,798,795]) ).
tff(890,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,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(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)],[889]) ).
tff(891,plain,
sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[890]) ).
tff(892,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x3,x5),sep(lseg(x1,x7),sep(lseg(x7,x12),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(893,plain,
sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x3,x5),sep(lseg(x1,x7),sep(lseg(x7,x12),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)],[892,7]) ).
tff(894,plain,
sep(lseg(x3,x5),sep(lseg(x1,x7),sep(lseg(x7,x12),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(x1,x7),sep(lseg(x3,x5),sep(lseg(x7,x12),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(symmetry,[status(thm)],[893]) ).
tff(895,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),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(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[888]) ).
tff(896,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),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(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[847]) ).
tff(897,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),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[896,849,895]) ).
tff(898,plain,
sep(lseg(x1,x7),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),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[897]) ).
tff(899,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x1,x7),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),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[898]) ).
tff(900,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),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),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[793]) ).
tff(901,plain,
sep(lseg(x7,x12),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,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[787]) ).
tff(902,plain,
sep(lseg(x7,x12),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(x7,x12),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)],[901,789,900]) ).
tff(903,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),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(x1,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),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)],[902]) ).
tff(904,plain,
sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),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,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)],[903]) ).
tff(905,plain,
sep(lseg(x5,x5),sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),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(x1,x7),sep(lseg(x7,x12),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)],[613,904]) ).
tff(906,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x5,x5),sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),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,x8),sep(lseg(x7,x12),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(907,plain,
sep(lseg(x5,x5),sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),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,x8),sep(lseg(x7,x12),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)],[906,199]) ).
tff(908,plain,
sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x5),sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x7,x12),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)],[907]) ).
tff(909,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),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(x1,x7),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),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[903,908,905,894,891,899]) ).
tff(910,plain,
sep(lseg(x3,x5),sep(lseg(x1,x7),sep(lseg(x7,x12),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(x5,x1),sep(lseg(x1,x7),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),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[701,909]) ).
tff(911,plain,
sep(lseg(x5,x1),sep(lseg(x1,x7),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),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x3,x5),sep(lseg(x1,x7),sep(lseg(x7,x12),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(symmetry,[status(thm)],[910]) ).
tff(912,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(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),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x1,x7),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),sep(lseg(x8,x11),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(913,plain,
sep(lseg(x1,x7),sep(lseg(x5,x1),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),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x1,x7),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),sep(lseg(x8,x11),emp)))))))))),
inference(unit_resolution,[status(thm)],[912,7]) ).
tff(914,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[763]) ).
tff(915,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[914]) ).
tff(916,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(917,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[916,7]) ).
tff(918,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[917]) ).
tff(919,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[918,915]) ).
tff(920,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = 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)],[919]) ).
tff(921,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,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[920]) ).
tff(922,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[921]) ).
tff(923,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),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),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[922]) ).
tff(924,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(925,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[924,7]) ).
tff(926,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[925]) ).
tff(927,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),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),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[926,923]) ).
tff(928,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x5,x1),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)],[927]) ).
tff(929,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[928]) ).
tff(930,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(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(931,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[930,7]) ).
tff(932,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[931]) ).
tff(933,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),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)],[927]) ).
tff(934,plain,
sep(lseg(x3,x5),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(x3,x5),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[933]) ).
tff(935,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(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(936,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[935,7]) ).
tff(937,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(938,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)],[937,7]) ).
tff(939,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)],[938]) ).
tff(940,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)],[939,762]) ).
tff(941,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(monotonicity,[status(thm)],[940]) ).
tff(942,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[941]) ).
tff(943,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))),
inference(transitivity,[status(thm)],[942,936]) ).
tff(944,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[943]) ).
tff(945,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),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)],[944]) ).
tff(946,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(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(947,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[946,7]) ).
tff(948,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))) = sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[947]) ).
tff(949,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),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)],[948,945]) ).
tff(950,plain,
sep(lseg(x3,x12),sep(lseg(x8,x11),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,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[949]) ).
tff(951,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),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,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[950]) ).
tff(952,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(x8,x11),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(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(953,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),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(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[952,7]) ).
tff(954,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),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)],[949]) ).
tff(955,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,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,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[954]) ).
tff(956,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),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(x3,x5),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[955]) ).
tff(957,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),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(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[956,953,951,934]) ).
tff(958,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[957]) ).
tff(959,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),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(transitivity,[status(thm)],[958,932,929]) ).
tff(960,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),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(x3,x5),sep(lseg(x5,x1),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)],[959]) ).
tff(961,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(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(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),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(962,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[961,7]) ).
tff(963,plain,
sep(lseg(x5,x1),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),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[897]) ).
tff(964,plain,
sep(lseg(x5,x1),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),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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(transitivity,[status(thm)],[963,962,960]) ).
tff(965,plain,
sep(lseg(x1,x7),sep(lseg(x5,x1),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),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[964]) ).
tff(966,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x1,x7),sep(lseg(x5,x1),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),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[965]) ).
tff(967,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,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(968,plain,
sep(lseg(x5,x1),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(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[967,7]) ).
tff(969,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)],[940]) ).
tff(970,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(971,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)],[970,7]) ).
tff(972,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)],[971]) ).
tff(973,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)],[972,969]) ).
tff(974,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)],[973]) ).
tff(975,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(976,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)],[975,7]) ).
tff(977,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)],[976]) ).
tff(978,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)],[977,974]) ).
tff(979,plain,
sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),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(monotonicity,[status(thm)],[978]) ).
tff(980,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(x8,x11),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[979]) ).
tff(981,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(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[980,968]) ).
tff(982,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(x7,x8),sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[981]) ).
tff(983,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),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(symmetry,[status(thm)],[982]) ).
tff(984,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,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(985,plain,
sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x5,x1),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(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[984,7]) ).
tff(986,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[985]) ).
tff(987,plain,
sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),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(transitivity,[status(thm)],[986,983]) ).
tff(988,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),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(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)],[987]) ).
tff(989,plain,
sep(lseg(x4,x12),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(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[988]) ).
tff(990,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(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(991,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[990,7]) ).
tff(992,plain,
sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))) = sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))),
inference(transitivity,[status(thm)],[744,763]) ).
tff(993,plain,
sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[992]) ).
tff(994,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))),
inference(symmetry,[status(thm)],[993]) ).
tff(995,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(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(996,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(unit_resolution,[status(thm)],[995,7]) ).
tff(997,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[996]) ).
tff(998,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[997,994]) ).
tff(999,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[998]) ).
tff(1000,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),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(transitivity,[status(thm)],[999,828,825]) ).
tff(1001,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),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(monotonicity,[status(thm)],[1000]) ).
tff(1002,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,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1003,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1002,7]) ).
tff(1004,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1003]) ).
tff(1005,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),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)],[1004,1001]) ).
tff(1006,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),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)],[1005]) ).
tff(1007,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(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1006]) ).
tff(1008,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[1007,991]) ).
tff(1009,plain,
sep(lseg(x4,x12),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(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[1008]) ).
tff(1010,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x12),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(symmetry,[status(thm)],[1009]) ).
tff(1011,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(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1012,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[1011,7]) ).
tff(1013,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)],[745]) ).
tff(1014,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[1013]) ).
tff(1015,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[1014]) ).
tff(1016,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(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1017,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[1016,7]) ).
tff(1018,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[1017]) ).
tff(1019,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[998]) ).
tff(1020,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1019,1018,1015]) ).
tff(1021,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1020]) ).
tff(1022,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(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1023,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1022,7]) ).
tff(1024,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1023]) ).
tff(1025,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1024,1021]) ).
tff(1026,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1025]) ).
tff(1027,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(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1028,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1027,7]) ).
tff(1029,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1028]) ).
tff(1030,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1029,1026]) ).
tff(1031,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1030]) ).
tff(1032,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[1031]) ).
tff(1033,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1034,plain,
sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[1033,7]) ).
tff(1035,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(x4,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1036,plain,
sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))),
inference(unit_resolution,[status(thm)],[1035,7]) ).
tff(1037,plain,
sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x4,x7),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)],[1036]) ).
tff(1038,plain,
sep(lseg(x6,x9),sep(lseg(x4,x12),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(transitivity,[status(thm)],[1037,745]) ).
tff(1039,plain,
sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[1038]) ).
tff(1040,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[1039]) ).
tff(1041,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1040,1034]) ).
tff(1042,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1041]) ).
tff(1043,plain,
sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1042]) ).
tff(1044,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1045,plain,
sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1044,7]) ).
tff(1046,plain,
sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),sep(lseg(x6,x9),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1045]) ).
tff(1047,plain,
sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1046,1043]) ).
tff(1048,plain,
sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1047]) ).
tff(1049,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1048]) ).
tff(1050,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1051,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1050,7]) ).
tff(1052,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1051]) ).
tff(1053,plain,
sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,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,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1047]) ).
tff(1054,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1053]) ).
tff(1055,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(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1056,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1055,7]) ).
tff(1057,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[919]) ).
tff(1058,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1057]) ).
tff(1059,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1058]) ).
tff(1060,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[1059,1056]) ).
tff(1061,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,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,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1060]) ).
tff(1062,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1061]) ).
tff(1063,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(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1064,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1063,7]) ).
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,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1066,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1065,7]) ).
tff(1067,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)],[1013]) ).
tff(1068,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[919]) ).
tff(1069,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,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(transitivity,[status(thm)],[1068,1067,783,780]) ).
tff(1070,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),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)],[1069]) ).
tff(1071,plain,
sep(lseg(x5,x1),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,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1070]) ).
tff(1072,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[1071,1066]) ).
tff(1073,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(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1072]) ).
tff(1074,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(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1073,1064,1062,1054]) ).
tff(1075,plain,
sep(lseg(x7,x8),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(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1074]) ).
tff(1076,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,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(x5,x1),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(1077,plain,
sep(lseg(x7,x8),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(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[1076,7]) ).
tff(1078,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x5,x1),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)],[1077]) ).
tff(1079,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),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(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1072]) ).
tff(1080,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[1079]) ).
tff(1081,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1082,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1081,7]) ).
tff(1083,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,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(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[921]) ).
tff(1084,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),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)],[1083]) ).
tff(1085,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(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1086,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1085,7]) ).
tff(1087,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1086]) ).
tff(1088,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),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)],[1087,1084]) ).
tff(1089,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),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)],[1088]) ).
tff(1090,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),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,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1089]) ).
tff(1091,plain,
sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),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)],[949]) ).
tff(1092,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,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(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1091]) ).
tff(1093,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),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(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1092]) ).
tff(1094,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),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)],[1093]) ).
tff(1095,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(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1096,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1095,7]) ).
tff(1097,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1096]) ).
tff(1098,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))) = sep(lseg(x5,x1),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)],[950]) ).
tff(1099,plain,
sep(lseg(x5,x1),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(x5,x1),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1098]) ).
tff(1100,plain,
sep(lseg(x5,x1),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(x5,x1),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)],[1099,1097,1094,1090,1082,1080]) ).
tff(1101,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[1100]) ).
tff(1102,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),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(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))),
inference(transitivity,[status(thm)],[1101,1078,1075,1052,1049,1032,1012,1010,989]) ).
tff(1103,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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,x12),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(monotonicity,[status(thm)],[1102]) ).
tff(1104,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x5,x1),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(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(x4,x12),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1106,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(unit_resolution,[status(thm)],[1105,7]) ).
tff(1107,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(1108,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)],[1107,7]) ).
tff(1109,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)],[969]) ).
tff(1110,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)],[1109,971]) ).
tff(1111,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)],[1110]) ).
tff(1112,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = 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)],[1111,1108]) ).
tff(1113,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(monotonicity,[status(thm)],[1112]) ).
tff(1114,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)],[1113]) ).
tff(1115,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)],[1114]) ).
tff(1116,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(1117,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)],[1116,7]) ).
tff(1118,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)],[1117]) ).
tff(1119,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)],[1111]) ).
tff(1120,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)],[1108]) ).
tff(1121,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)],[1120,1119]) ).
tff(1122,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)],[1121]) ).
tff(1123,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(x8,x11),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1122]) ).
tff(1124,plain,
sep(lseg(x7,x12),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(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(monotonicity,[status(thm)],[1123]) ).
tff(1125,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,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(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[866]) ).
tff(1126,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,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1127,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1126,7]) ).
tff(1128,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1127]) ).
tff(1129,plain,
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(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[830]) ).
tff(1130,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(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1129]) ).
tff(1131,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(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)],[1130,1128,1125,1124,1118,1115]) ).
tff(1132,plain,
sep(lseg(x5,x1),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(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)],[1131]) ).
tff(1133,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(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(x5,x1),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(1134,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(x8,x11),emp)))))))) = sep(lseg(x5,x1),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)],[1133,7]) ).
tff(1135,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(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1129]) ).
tff(1136,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,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(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1135]) ).
tff(1137,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(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1138,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1137,7]) ).
tff(1139,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),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(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[829]) ).
tff(1140,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,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(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1139]) ).
tff(1141,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(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x6,x9),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1140]) ).
tff(1142,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(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(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1141,1138,1136]) ).
tff(1143,plain,
sep(lseg(x7,x8),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(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(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1142]) ).
tff(1144,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(1145,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)],[1144,7]) ).
tff(1146,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)],[838]) ).
tff(1147,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(x3,x5),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)],[1146,1145]) ).
tff(1148,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(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(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1147]) ).
tff(1149,plain,
sep(lseg(x7,x12),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,x12),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)],[1148]) ).
tff(1150,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(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x8),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(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1149]) ).
tff(1151,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(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,x12),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(quant_inst,[status(thm)],]) ).
tff(1152,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(x8,x11),sep(lseg(x6,x9),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(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[1151,7]) ).
tff(1153,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(x8,x11),sep(lseg(x6,x9),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(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[1152]) ).
tff(1154,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)],[1146]) ).
tff(1155,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)],[1145]) ).
tff(1156,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)],[1155,1154]) ).
tff(1157,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)],[1156]) ).
tff(1158,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(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)],[1157]) ).
tff(1159,plain,
sep(lseg(x7,x12),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(x7,x12),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(monotonicity,[status(thm)],[1158]) ).
tff(1160,plain,
sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x12),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)],[987]) ).
tff(1161,plain,
sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),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(transitivity,[status(thm)],[1160,1159,1153,1150,1143,1134,1132]) ).
tff(1162,plain,
sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x4,x12),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)],[1161]) ).
tff(1163,plain,
sep(lseg(x4,x12),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(x4,x12),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),emp))))))))),
inference(symmetry,[status(thm)],[1162]) ).
tff(1164,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,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),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(1165,plain,
sep(lseg(x7,x12),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,x12),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)],[1164,7]) ).
tff(1166,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),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(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1165]) ).
tff(1167,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),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(x3,x5),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1166,1149]) ).
tff(1168,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x7,x12),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)],[1167]) ).
tff(1169,plain,
sep(lseg(x7,x8),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(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[1168]) ).
tff(1170,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(x8,x11),emp)))))))) = sep(lseg(x7,x8),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(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1143]) ).
tff(1171,plain,
sep(lseg(x5,x1),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(x5,x1),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(symmetry,[status(thm)],[1134]) ).
tff(1172,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(x5,x1),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(symmetry,[status(thm)],[1132]) ).
tff(1173,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(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[1172,1171,1170,1169]) ).
tff(1174,plain,
sep(lseg(x4,x12),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(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[1173]) ).
tff(1175,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x4,x12),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(symmetry,[status(thm)],[1174]) ).
tff(1176,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(x7,x12),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(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),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(1177,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[1176,7]) ).
tff(1178,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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,x5),sep(lseg(x7,x12),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)],[1177]) ).
tff(1179,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(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(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[823,814,812]) ).
tff(1180,plain,
sep(lseg(x5,x1),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(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(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1179]) ).
tff(1181,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(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(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(1182,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(x8,x11),emp)))))))) = sep(lseg(x5,x1),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(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1181,7]) ).
tff(1183,plain,
sep(lseg(x4,x12),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(x8,x11),emp)))))))) = 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(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1142]) ).
tff(1184,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x12),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(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1167]) ).
tff(1185,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x7,x12),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)],[1184,1183,1182,1180]) ).
tff(1186,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x7,x12),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)],[1185]) ).
tff(1187,plain,
sep(lseg(x7,x8),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(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),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)],[1186]) ).
tff(1188,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1042,1045]) ).
tff(1189,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1188]) ).
tff(1190,plain,
sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1189]) ).
tff(1191,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1192,plain,
sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1191,7]) ).
tff(1193,plain,
sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1192]) ).
tff(1194,plain,
sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1193,1190]) ).
tff(1195,plain,
sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1194]) ).
tff(1196,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1195]) ).
tff(1197,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(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1198,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1197,7]) ).
tff(1199,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1025]) ).
tff(1200,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1199]) ).
tff(1201,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[1200,1198]) ).
tff(1202,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[1201]) ).
tff(1203,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1202]) ).
tff(1204,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(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1205,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[1204,7]) ).
tff(1206,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),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(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1005]) ).
tff(1207,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(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1208,plain,
sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1207,7]) ).
tff(1209,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1208]) ).
tff(1210,plain,
sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),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(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1209,1206]) ).
tff(1211,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x12),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(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1210]) ).
tff(1212,plain,
sep(lseg(x4,x12),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(x8,x11),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[1211]) ).
tff(1213,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(x8,x11),emp)))))))) = sep(lseg(x4,x12),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(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1183]) ).
tff(1214,plain,
sep(lseg(x5,x1),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(x8,x11),emp)))))))) = 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(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1182]) ).
tff(1215,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(x8,x11),emp)))))))) = sep(lseg(x5,x1),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(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1180]) ).
tff(1216,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(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1215,1214,1213,1212,1205,1203,1196]) ).
tff(1217,plain,
sep(lseg(x7,x8),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(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1216]) ).
tff(1218,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,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,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1217]) ).
tff(1219,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1220,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1219,7]) ).
tff(1221,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(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1222,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1221,7]) ).
tff(1223,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[1088]) ).
tff(1224,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),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(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1223]) ).
tff(1225,plain,
sep(lseg(x7,x12),sep(lseg(x5,x1),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(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[1224,1222]) ).
tff(1226,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[1225]) ).
tff(1227,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[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(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1229,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[1228,7]) ).
tff(1230,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[1229]) ).
tff(1231,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1056]) ).
tff(1232,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1231,1058]) ).
tff(1233,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1232]) ).
tff(1234,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,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1235,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1234,7]) ).
tff(1236,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1235]) ).
tff(1237,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1236,1233]) ).
tff(1238,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1237]) ).
tff(1239,plain,
sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[1238]) ).
tff(1240,plain,
sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,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(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1194]) ).
tff(1241,plain,
sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[1240,1239,1230,1227]) ).
tff(1242,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[1241]) ).
tff(1243,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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,x8),sep(lseg(x6,x9),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1242]) ).
tff(1244,plain,
lseg(x5,x12) = lseg(x3,x12),
inference(monotonicity,[status(thm)],[612]) ).
tff(1245,plain,
sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[1244]) ).
tff(1246,plain,
sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x5,x1),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(transitivity,[status(thm)],[1245,1243,1220,1218,1187,1178,1175,1163,1106,1104]) ).
tff(1247,plain,
x1 = x3,
inference(transitivity,[status(thm)],[699,612]) ).
tff(1248,plain,
lseg(x1,x7) = lseg(x3,x7),
inference(monotonicity,[status(thm)],[1247]) ).
tff(1249,plain,
lseg(x3,x7) = lseg(x1,x7),
inference(symmetry,[status(thm)],[1248]) ).
tff(1250,plain,
lseg(x5,x8) = lseg(x1,x7),
inference(transitivity,[status(thm)],[676,1249]) ).
tff(1251,plain,
sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,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(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)],[1250,1246]) ).
tff(1252,plain,
sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,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,x12),sep(lseg(x3,x5),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)],[1251,966,913,911,894,891]) ).
tff(1253,plain,
( heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))
<=> heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[1252]) ).
tff(1254,plain,
( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))
<=> heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[1253]) ).
tff(1255,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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,x12),sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(1256,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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,x12),sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1255,7]) ).
tff(1257,plain,
sep(lseg(x7,x12),sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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(symmetry,[status(thm)],[1256]) ).
tff(1258,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x1,x7),sep(lseg(x5,x1),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(1259,plain,
sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x1,x7),sep(lseg(x5,x1),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)],[1258,7]) ).
tff(1260,plain,
sep(lseg(x3,x5),sep(lseg(x1,x7),sep(lseg(x5,x1),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(x1,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(symmetry,[status(thm)],[1259]) ).
tff(1261,plain,
sep(lseg(x1,x7),sep(lseg(x5,x1),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(x1,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[1100]) ).
tff(1262,plain,
sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),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,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)],[1261]) ).
tff(1263,plain,
sep(lseg(x5,x5),sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x1,x7),sep(lseg(x5,x1),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)],[613,1262]) ).
tff(1264,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x5,x5),sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),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,x8),sep(lseg(x5,x1),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(1265,plain,
sep(lseg(x5,x5),sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),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,x8),sep(lseg(x5,x1),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)],[1264,199]) ).
tff(1266,plain,
sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x5,x5),sep(lseg(x1,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),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)],[1265]) ).
tff(1267,plain,
sep(lseg(x1,x7),sep(lseg(x5,x1),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(x1,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(transitivity,[status(thm)],[1261,1266,1263,1260]) ).
tff(1268,plain,
sep(lseg(x7,x12),sep(lseg(x1,x7),sep(lseg(x5,x1),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,x12),sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1267]) ).
tff(1269,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),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,x12),sep(lseg(x1,x7),sep(lseg(x5,x1),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(1270,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),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,x12),sep(lseg(x1,x7),sep(lseg(x5,x1),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)],[1269,7]) ).
tff(1271,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),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(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[1270,1268,1257,966,913,911,894,891]) ).
tff(1272,plain,
( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),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))))))))))
<=> heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),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)],[1271]) ).
tff(1273,plain,
sep(lseg(x7,x12),sep(lseg(x1,x7),sep(lseg(x5,x1),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(x1,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),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(symmetry,[status(thm)],[1270]) ).
tff(1274,plain,
sep(lseg(x7,x12),sep(lseg(x1,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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,x12),sep(lseg(x1,x7),sep(lseg(x5,x1),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(symmetry,[status(thm)],[1268]) ).
tff(1275,plain,
sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x1,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),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(transitivity,[status(thm)],[1256,1274,1273]) ).
tff(1276,plain,
( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)))))))))))
<=> heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[1275]) ).
tff(1277,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(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(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(1278,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(x1,x6),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)],[1277,7]) ).
tff(1279,plain,
sep(lseg(x1,x6),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(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)],[1278]) ).
tff(1280,plain,
sep(lseg(x1,x6),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(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)],[1279,84]) ).
tff(1281,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),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(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)],[1280]) ).
tff(1282,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(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(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(1283,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),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(x1,x6),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)],[1282,7]) ).
tff(1284,plain,
sep(lseg(x1,x6),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(x1,x6),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)],[1283]) ).
tff(1285,plain,
sep(lseg(x1,x6),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(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)],[1284,1281]) ).
tff(1286,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),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(x5,x1),sep(lseg(x3,x5),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)],[1285]) ).
tff(1287,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(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(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(1288,plain,
sep(lseg(x7,x12),sep(lseg(x1,x6),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(x1,x6),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(unit_resolution,[status(thm)],[1287,7]) ).
tff(1289,plain,
sep(lseg(x1,x6),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(x1,x6),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)],[1288]) ).
tff(1290,plain,
sep(lseg(x1,x6),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(x5,x1),sep(lseg(x3,x5),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)],[1289,1286]) ).
tff(1291,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),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,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[1290]) ).
tff(1292,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(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(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(1293,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),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(x1,x6),sep(lseg(x7,x8),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(unit_resolution,[status(thm)],[1292,7]) ).
tff(1294,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),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,x8),sep(lseg(x1,x6),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)],[1293]) ).
tff(1295,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),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,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[1294,1291]) ).
tff(1296,plain,
sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),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(x4,x12),sep(lseg(x7,x8),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),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)],[1295]) ).
tff(1297,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(x7,x8),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(x1,x6),sep(lseg(x4,x12),sep(lseg(x7,x8),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(quant_inst,[status(thm)],]) ).
tff(1298,plain,
sep(lseg(x4,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),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(x1,x6),sep(lseg(x4,x12),sep(lseg(x7,x8),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(unit_resolution,[status(thm)],[1297,7]) ).
tff(1299,plain,
sep(lseg(x1,x6),sep(lseg(x4,x12),sep(lseg(x7,x8),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(x4,x12),sep(lseg(x1,x6),sep(lseg(x7,x8),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)],[1298]) ).
tff(1300,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(1301,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)],[1300,7]) ).
tff(1302,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)],[204]) ).
tff(1303,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)],[1302]) ).
tff(1304,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)],[1303]) ).
tff(1305,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(1306,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)],[1305,7]) ).
tff(1307,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)],[1306]) ).
tff(1308,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)],[1307,1304]) ).
tff(1309,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)],[1308]) ).
tff(1310,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)],[1309]) ).
tff(1311,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)],[1310]) ).
tff(1312,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(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)],[1311,1301]) ).
tff(1313,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(monotonicity,[status(thm)],[1312]) ).
tff(1314,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(symmetry,[status(thm)],[1313]) ).
tff(1315,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,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(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(1316,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(x3,x5),sep(lseg(x7,x12),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)],[1315,7]) ).
tff(1317,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),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(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)],[1316]) ).
tff(1318,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),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(transitivity,[status(thm)],[1317,1314]) ).
tff(1319,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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(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)],[1318]) ).
tff(1320,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(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(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),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(1321,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),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)],[1320,7]) ).
tff(1322,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),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(x3,x5),sep(lseg(x7,x12),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)],[1321]) ).
tff(1323,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(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(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(1324,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),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(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)],[1323,7]) ).
tff(1325,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)],[1308]) ).
tff(1326,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(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1325]) ).
tff(1327,plain,
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(x4,x7),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1326]) ).
tff(1328,plain,
sep(lseg(x5,x1),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(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)],[1327]) ).
tff(1329,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(x6,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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1330,plain,
sep(lseg(x5,x1),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(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)],[1329,7]) ).
tff(1331,plain,
sep(lseg(x7,x8),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(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)],[1330]) ).
tff(1332,plain,
sep(lseg(x7,x8),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(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)],[1331,1328]) ).
tff(1333,plain,
sep(lseg(x7,x12),sep(lseg(x7,x8),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(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)],[1332]) ).
tff(1334,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(x6,x7),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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1333]) ).
tff(1335,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(x6,x7),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x7,x12),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)],[1334,1324]) ).
tff(1336,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(x6,x7),sep(lseg(x8,x11),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x7,x12),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)],[1335]) ).
tff(1337,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(x6,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(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1333]) ).
tff(1338,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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1339,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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1338,7]) ).
tff(1340,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(x6,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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1339]) ).
tff(1341,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(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(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)],[1340,1337,1336,1322,1319]) ).
tff(1342,plain,
sep(lseg(x4,x12),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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),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)],[1341]) ).
tff(1343,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(x7,x8),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(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),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(1344,plain,
sep(lseg(x4,x12),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(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(x7,x8),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)],[1343,7]) ).
tff(1345,plain,
sep(lseg(x7,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),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(x4,x12),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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(symmetry,[status(thm)],[1344]) ).
tff(1346,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(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(monotonicity,[status(thm)],[1312]) ).
tff(1347,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(symmetry,[status(thm)],[1346]) ).
tff(1348,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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),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(1349,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(x3,x5),sep(lseg(x7,x8),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)],[1348,7]) ).
tff(1350,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),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(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)],[1349]) ).
tff(1351,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),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(transitivity,[status(thm)],[1350,1347]) ).
tff(1352,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),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(x4,x12),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)],[1351]) ).
tff(1353,plain,
sep(lseg(x4,x12),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(x4,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),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)],[1352]) ).
tff(1354,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(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1355,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[1354,7]) ).
tff(1356,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)],[1302]) ).
tff(1357,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(1358,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)],[1357,7]) ).
tff(1359,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)],[1358]) ).
tff(1360,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)],[1359,1356]) ).
tff(1361,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)],[1360]) ).
tff(1362,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)],[1361]) ).
tff(1363,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(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1362]) ).
tff(1364,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),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(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1363]) ).
tff(1365,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(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(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1366,plain,
sep(lseg(x3,x5),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(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1365,7]) ).
tff(1367,plain,
sep(lseg(x3,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(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1366]) ).
tff(1368,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),sep(lseg(x6,x7),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1369,plain,
sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))),
inference(unit_resolution,[status(thm)],[1368,7]) ).
tff(1370,plain,
sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))) = sep(lseg(x6,x9),sep(lseg(x8,x11),sep(lseg(x6,x7),emp))),
inference(symmetry,[status(thm)],[254]) ).
tff(1371,plain,
sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))) = sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))),
inference(transitivity,[status(thm)],[1370,258]) ).
tff(1372,plain,
sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),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)],[1371]) ).
tff(1373,plain,
sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) = sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))),
inference(symmetry,[status(thm)],[1372]) ).
tff(1374,plain,
sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))) = sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))),
inference(transitivity,[status(thm)],[1359,1356,1373,1369]) ).
tff(1375,plain,
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(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))),
inference(monotonicity,[status(thm)],[1374]) ).
tff(1376,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = 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)],[1375]) ).
tff(1377,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(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1378,plain,
sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))),
inference(unit_resolution,[status(thm)],[1377,7]) ).
tff(1379,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))),
inference(symmetry,[status(thm)],[1378]) ).
tff(1380,plain,
sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))) = sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1379,1376]) ).
tff(1381,plain,
sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x3,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)],[1380]) ).
tff(1382,plain,
sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),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(transitivity,[status(thm)],[1381,1367,1364]) ).
tff(1383,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),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(monotonicity,[status(thm)],[1382]) ).
tff(1384,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(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1385,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(unit_resolution,[status(thm)],[1384,7]) ).
tff(1386,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(symmetry,[status(thm)],[1385]) ).
tff(1387,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),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)],[1386,1383]) ).
tff(1388,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),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)],[1387]) ).
tff(1389,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(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(symmetry,[status(thm)],[1388]) ).
tff(1390,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(transitivity,[status(thm)],[1389,1355]) ).
tff(1391,plain,
sep(lseg(x4,x12),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(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))),
inference(monotonicity,[status(thm)],[1390]) ).
tff(1392,plain,
sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x4,x12),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(symmetry,[status(thm)],[1391]) ).
tff(1393,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(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1394,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x4,x12),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))),
inference(unit_resolution,[status(thm)],[1393,7]) ).
tff(1395,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,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[1360]) ).
tff(1396,plain,
sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),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)],[1395]) ).
tff(1397,plain,
sep(lseg(x3,x5),sep(lseg(x4,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(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1396]) ).
tff(1398,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,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1397]) ).
tff(1399,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(1400,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)],[1399,7]) ).
tff(1401,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)],[1400]) ).
tff(1402,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),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(monotonicity,[status(thm)],[1380]) ).
tff(1403,plain,
sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1402,1401,1398]) ).
tff(1404,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1403]) ).
tff(1405,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(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1406,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(unit_resolution,[status(thm)],[1405,7]) ).
tff(1407,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(symmetry,[status(thm)],[1406]) ).
tff(1408,plain,
sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1407,1404]) ).
tff(1409,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1408]) ).
tff(1410,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(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1411,plain,
sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[1410,7]) ).
tff(1412,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(symmetry,[status(thm)],[1411]) ).
tff(1413,plain,
sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1412,1409]) ).
tff(1414,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1413]) ).
tff(1415,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))),
inference(symmetry,[status(thm)],[1414]) ).
tff(1416,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(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1417,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1416,7]) ).
tff(1418,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(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1419,plain,
sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[1418,7]) ).
tff(1420,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x4,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)],[1419]) ).
tff(1421,plain,
sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1420,1395]) ).
tff(1422,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,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(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1421]) ).
tff(1423,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1422]) ).
tff(1424,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))) = sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1423,1417]) ).
tff(1425,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1424]) ).
tff(1426,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,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,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1425]) ).
tff(1427,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(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1428,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1427,7]) ).
tff(1429,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x1),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1428]) ).
tff(1430,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1429,1426]) ).
tff(1431,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1430]) ).
tff(1432,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1431]) ).
tff(1433,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1434,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(unit_resolution,[status(thm)],[1433,7]) ).
tff(1435,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),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(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(symmetry,[status(thm)],[1434]) ).
tff(1436,plain,
sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,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,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1430]) ).
tff(1437,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1436]) ).
tff(1438,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(x4,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(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1439,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,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(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1438,7]) ).
tff(1440,plain,
sep(lseg(x4,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(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[1302]) ).
tff(1441,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(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(symmetry,[status(thm)],[1440]) ).
tff(1442,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,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1443,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,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(unit_resolution,[status(thm)],[1442,7]) ).
tff(1444,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,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(symmetry,[status(thm)],[1443]) ).
tff(1445,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1444,1441]) ).
tff(1446,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),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(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1445]) ).
tff(1447,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x4,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,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1446]) ).
tff(1448,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1447]) ).
tff(1449,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1448,1439]) ).
tff(1450,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1449]) ).
tff(1451,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),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,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1450]) ).
tff(1452,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(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),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,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1453,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),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,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1452,7]) ).
tff(1454,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,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1455,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1454,7]) ).
tff(1456,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(x3,x12),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1362]) ).
tff(1457,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(symmetry,[status(thm)],[1456]) ).
tff(1458,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(1459,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)],[1458,7]) ).
tff(1460,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)],[1459]) ).
tff(1461,plain,
sep(lseg(x3,x12),sep(lseg(x4,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(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1396]) ).
tff(1462,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1445]) ).
tff(1463,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x4,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)],[1462,1461,1460,1457]) ).
tff(1464,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x7),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,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1463]) ).
tff(1465,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,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1464]) ).
tff(1466,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,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1465,1455]) ).
tff(1467,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,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1466]) ).
tff(1468,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(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1467,1453,1451,1437]) ).
tff(1469,plain,
sep(lseg(x7,x8),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,x8),sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1468]) ).
tff(1470,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,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(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(1471,plain,
sep(lseg(x7,x8),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,x8),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)],[1470,7]) ).
tff(1472,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),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,x8),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)],[1471]) ).
tff(1473,plain,
sep(lseg(x7,x8),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,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1466]) ).
tff(1474,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),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,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1473]) ).
tff(1475,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1476,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(unit_resolution,[status(thm)],[1475,7]) ).
tff(1477,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,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,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1445]) ).
tff(1478,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x7),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(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1477]) ).
tff(1479,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(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,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1480,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x7),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,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(unit_resolution,[status(thm)],[1479,7]) ).
tff(1481,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),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(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1480]) ).
tff(1482,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),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(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1481,1478]) ).
tff(1483,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1482]) ).
tff(1484,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,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(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1483]) ).
tff(1485,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(1486,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)],[1485,7]) ).
tff(1487,plain,
sep(lseg(x7,x8),sep(lseg(x4,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(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1396]) ).
tff(1488,plain,
sep(lseg(x7,x8),sep(lseg(x4,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(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1487,1486]) ).
tff(1489,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,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(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1488]) ).
tff(1490,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,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(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1489]) ).
tff(1491,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),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(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1490]) ).
tff(1492,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(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,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(quant_inst,[status(thm)],]) ).
tff(1493,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),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(x5,x1),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(unit_resolution,[status(thm)],[1492,7]) ).
tff(1494,plain,
sep(lseg(x5,x1),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(x5,x1),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)],[1493]) ).
tff(1495,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1488]) ).
tff(1496,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,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1495]) ).
tff(1497,plain,
sep(lseg(x5,x1),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(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1496]) ).
tff(1498,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1497]) ).
tff(1499,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(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)],[1498,1494,1491,1484,1476,1474]) ).
tff(1500,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(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)],[1499]) ).
tff(1501,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(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)],[1500,1472,1469,1435,1432,1415,1394,1392,1353]) ).
tff(1502,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x7,x8),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)],[1501]) ).
tff(1503,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),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(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1421]) ).
tff(1504,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(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(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1505,plain,
sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x4,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(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(unit_resolution,[status(thm)],[1504,7]) ).
tff(1506,plain,
sep(lseg(x6,x7),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(x6,x7),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(symmetry,[status(thm)],[1505]) ).
tff(1507,plain,
sep(lseg(x6,x7),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(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1506,1503]) ).
tff(1508,plain,
sep(lseg(x3,x12),sep(lseg(x6,x7),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,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1507]) ).
tff(1509,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(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x7),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(1510,plain,
sep(lseg(x3,x12),sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x6,x7),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)],[1509,7]) ).
tff(1511,plain,
sep(lseg(x6,x7),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(x3,x12),sep(lseg(x6,x7),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)],[1510]) ).
tff(1512,plain,
sep(lseg(x6,x7),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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1511,1508]) ).
tff(1513,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),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(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1512]) ).
tff(1514,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(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(x6,x7),sep(lseg(x5,x1),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(1515,plain,
sep(lseg(x5,x1),sep(lseg(x6,x7),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(x6,x7),sep(lseg(x5,x1),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)],[1514,7]) ).
tff(1516,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),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(x5,x1),sep(lseg(x6,x7),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(symmetry,[status(thm)],[1515]) ).
tff(1517,plain,
sep(lseg(x6,x7),sep(lseg(x5,x1),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(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))),
inference(transitivity,[status(thm)],[1516,1513]) ).
tff(1518,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(monotonicity,[status(thm)],[1517]) ).
tff(1519,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(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(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(1520,plain,
sep(lseg(x3,x5),sep(lseg(x6,x7),sep(lseg(x5,x1),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(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1519,7]) ).
tff(1521,plain,
sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x6,x7),sep(lseg(x5,x1),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(symmetry,[status(thm)],[1520]) ).
tff(1522,plain,
sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp))))))))),
inference(transitivity,[status(thm)],[1521,1518]) ).
tff(1523,plain,
sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))))))))),
inference(monotonicity,[status(thm)],[1522]) ).
tff(1524,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(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(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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(1525,plain,
sep(lseg(x7,x12),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1524,7]) ).
tff(1526,plain,
sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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,x12),sep(lseg(x6,x7),sep(lseg(x3,x5),sep(lseg(x5,x1),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(symmetry,[status(thm)],[1525]) ).
tff(1527,plain,
sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x4,x12),sep(lseg(x7,x8),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(transitivity,[status(thm)],[1526,1523,1502,1345,1342]) ).
tff(1528,plain,
sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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(x1,x6),sep(lseg(x4,x12),sep(lseg(x7,x8),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)],[1527]) ).
tff(1529,plain,
sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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(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)],[1528,1299,1296,61,58,38,35,25]) ).
tff(1530,plain,
( heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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))))))))))))
<=> 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)],[1529]) ).
tff(1531,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(x3,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)],[1530]) ).
tff(1532,plain,
heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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(modus_ponens,[status(thm)],[170,1531]) ).
tff(1533,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1534,plain,
( ( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)))))))))))
| ( 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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1535,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(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)],[1534]) ).
tff(1536,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,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)],[1535,1533]) ).
tff(1537,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(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(1538,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,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(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[1537,1536]) ).
tff(1539,plain,
( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)))))))))))
| ~ heap(sep(lseg(x1,x6),sep(lseg(x6,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1538,590,279]) ).
tff(1540,plain,
heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1539,1532]) ).
tff(1541,plain,
heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x5,x1),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(modus_ponens,[status(thm)],[1540,1276]) ).
tff(1542,plain,
heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))))),
inference(modus_ponens,[status(thm)],[1541,1272]) ).
tff(1543,plain,
heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))),
inference(modus_ponens,[status(thm)],[1542,1254]) ).
tff(1544,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x8 )
| ( x5 = x12 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),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))) )
| ( x5 = x8 )
| ( x5 = x12 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1545,plain,
( ( ( x5 = x12 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) )
<=> ( ( x5 = x8 )
| ( x5 = x12 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1546,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x12 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),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))) )
| ( x5 = x8 )
| ( x5 = x12 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[1545]) ).
tff(1547,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x12 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),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))) )
| ( x5 = x8 )
| ( x5 = x12 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[1546,1544]) ).
tff(1548,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x12 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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(1549,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x8 )
| ( x5 = x12 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[1548,1547]) ).
tff(1550,plain,
( ( x5 = x12 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x12),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x5,x1),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)],[1549,184,693]) ).
tff(1551,plain,
x5 = x12,
inference(unit_resolution,[status(thm)],[1550,1543]) ).
tff(1552,plain,
x12 = x5,
inference(symmetry,[status(thm)],[1551]) ).
tff(1553,plain,
lseg(x3,x12) = lseg(x3,x5),
inference(monotonicity,[status(thm)],[1552]) ).
tff(1554,plain,
sep(lseg(x3,x12),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,x5),sep(lseg(x5,x1),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)],[1553,741]) ).
tff(1555,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))) = sep(lseg(x3,x12),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)],[1554]) ).
tff(1556,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x6,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,x5),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[654]) ).
tff(1557,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x6,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[643]) ).
tff(1558,plain,
sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(transitivity,[status(thm)],[640,1557,651,1556,657,722,725,728,1555,736,708]) ).
tff(1559,plain,
( heap(sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp))))))))
<=> heap(sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) ),
inference(monotonicity,[status(thm)],[1558]) ).
tff(1560,plain,
( heap(sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))))
<=> heap(sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),emp)))))))) ),
inference(symmetry,[status(thm)],[1559]) ).
tff(1561,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(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1562,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[1561,7]) ).
tff(1563,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1232]) ).
tff(1564,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(x4,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(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1565,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,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(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1564,7]) ).
tff(1566,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,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(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1565]) ).
tff(1567,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1566,1563]) ).
tff(1568,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1567]) ).
tff(1569,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),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(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[1568]) ).
tff(1570,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x5,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1571,plain,
sep(lseg(x5,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1570,199]) ).
tff(1572,plain,
sep(lseg(x5,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[613,1088]) ).
tff(1573,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x5,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1572]) ).
tff(1574,plain,
sep(lseg(x5,x1),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(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[1083,1086]) ).
tff(1575,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1574]) ).
tff(1576,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1575]) ).
tff(1577,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1563]) ).
tff(1578,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1577,1565,1576,1573,1571,1087,1084]) ).
tff(1579,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,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(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1553,1578]) ).
tff(1580,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),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,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(symmetry,[status(thm)],[1579]) ).
tff(1581,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(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1582,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1581,7]) ).
tff(1583,plain,
sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))),
inference(monotonicity,[status(thm)],[215]) ).
tff(1584,plain,
sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))) = sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))),
inference(transitivity,[status(thm)],[1583,918,915]) ).
tff(1585,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(monotonicity,[status(thm)],[1584]) ).
tff(1586,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1587,plain,
sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[1586,7]) ).
tff(1588,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x7),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[1587]) ).
tff(1589,plain,
sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))),
inference(symmetry,[status(thm)],[216]) ).
tff(1590,plain,
sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[1589]) ).
tff(1591,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x4,x7),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[210]) ).
tff(1592,plain,
sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))),
inference(transitivity,[status(thm)],[1591,1590,1588,1585]) ).
tff(1593,plain,
sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(monotonicity,[status(thm)],[1592]) ).
tff(1594,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1593]) ).
tff(1595,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))) = sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[1594,1582]) ).
tff(1596,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1595]) ).
tff(1597,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1596]) ).
tff(1598,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(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1599,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1598,7]) ).
tff(1600,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1599]) ).
tff(1601,plain,
sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))) = sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))),
inference(transitivity,[status(thm)],[210,1589]) ).
tff(1602,plain,
sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[1601]) ).
tff(1603,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[1602]) ).
tff(1604,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1605,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[1604,7]) ).
tff(1606,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[1605]) ).
tff(1607,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[1606,1603]) ).
tff(1608,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[1607]) ).
tff(1609,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1608]) ).
tff(1610,plain,
x4 = x3,
inference(transitivity,[status(thm)],[189,1552,612]) ).
tff(1611,plain,
lseg(x4,x8) = lseg(x3,x7),
inference(monotonicity,[status(thm)],[1610,285]) ).
tff(1612,plain,
lseg(x4,x7) = lseg(x4,x8),
inference(monotonicity,[status(thm)],[284]) ).
tff(1613,plain,
lseg(x4,x7) = lseg(x3,x7),
inference(transitivity,[status(thm)],[1612,1611]) ).
tff(1614,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1613,1609]) ).
tff(1615,plain,
sep(lseg(x3,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1614]) ).
tff(1616,plain,
lseg(x6,x7) = lseg(x6,x8),
inference(monotonicity,[status(thm)],[284]) ).
tff(1617,plain,
lseg(x6,x8) = lseg(x6,x7),
inference(symmetry,[status(thm)],[1616]) ).
tff(1618,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)],[318]) ).
tff(1619,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(1620,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)],[1619,7]) ).
tff(1621,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)],[1620]) ).
tff(1622,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)],[1621,1618]) ).
tff(1623,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)],[1622]) ).
tff(1624,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(1625,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)],[1624,7]) ).
tff(1626,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)],[1625]) ).
tff(1627,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)],[1626,1623]) ).
tff(1628,plain,
sep(lseg(x7,x12),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(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)],[1627]) ).
tff(1629,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(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,x12),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(1630,plain,
sep(lseg(x7,x12),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,x12),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)],[1629,7]) ).
tff(1631,plain,
sep(lseg(x1,x6),sep(lseg(x7,x12),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(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)],[1630]) ).
tff(1632,plain,
sep(lseg(x1,x6),sep(lseg(x7,x12),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(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)],[1631,1628]) ).
tff(1633,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),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(monotonicity,[status(thm)],[1632]) ).
tff(1634,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(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,x12),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(1635,plain,
sep(lseg(x5,x1),sep(lseg(x1,x6),sep(lseg(x7,x12),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,x12),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)],[1634,7]) ).
tff(1636,plain,
sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),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,x12),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)],[1635]) ).
tff(1637,plain,
sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),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)],[1636,1633]) ).
tff(1638,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),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)],[1637]) ).
tff(1639,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(x5,x1),sep(lseg(x7,x12),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(x5,x1),sep(lseg(x7,x12),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(1640,plain,
sep(lseg(x7,x8),sep(lseg(x1,x6),sep(lseg(x5,x1),sep(lseg(x7,x12),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(x5,x1),sep(lseg(x7,x12),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)],[1639,7]) ).
tff(1641,plain,
sep(lseg(x1,x6),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),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(x5,x1),sep(lseg(x7,x12),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)],[1640]) ).
tff(1642,plain,
sep(lseg(x7,x12),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(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))),
inference(monotonicity,[status(thm)],[269]) ).
tff(1643,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x7,x12),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)],[1642]) ).
tff(1644,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1645,plain,
sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))),
inference(unit_resolution,[status(thm)],[1644,7]) ).
tff(1646,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))),
inference(symmetry,[status(thm)],[1645]) ).
tff(1647,plain,
sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))) = sep(lseg(x7,x12),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)],[1646,1643]) ).
tff(1648,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x3,x5),sep(lseg(x4,x12),sep(lseg(x6,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1647]) ).
tff(1649,plain,
sep(lseg(x5,x1),sep(lseg(x7,x12),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(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))),
inference(symmetry,[status(thm)],[1648]) ).
tff(1650,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),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(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(monotonicity,[status(thm)],[1649]) ).
tff(1651,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),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)],[1650]) ).
tff(1652,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1653,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(unit_resolution,[status(thm)],[1652,7]) ).
tff(1654,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(symmetry,[status(thm)],[1653]) ).
tff(1655,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x7,x12),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)],[1654,1651]) ).
tff(1656,plain,
lseg(x1,x6) = lseg(x5,x6),
inference(monotonicity,[status(thm)],[699]) ).
tff(1657,plain,
lseg(x5,x6) = lseg(x1,x6),
inference(symmetry,[status(thm)],[1656]) ).
tff(1658,plain,
sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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(x5,x1),sep(lseg(x7,x12),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)],[1657,1655]) ).
tff(1659,plain,
sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) = sep(lseg(x7,x8),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(transitivity,[status(thm)],[1658,1641,1638,315]) ).
tff(1660,plain,
sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x8),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)],[676,1659]) ).
tff(1661,plain,
( heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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,x8),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)],[1660]) ).
tff(1662,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x8),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)))))))))))
<=> heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ),
inference(symmetry,[status(thm)],[1661]) ).
tff(1663,plain,
heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))),
inference(modus_ponens,[status(thm)],[599,1662]) ).
tff(1664,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x8 )
| ( x5 = x6 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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))) )
| ( x5 = x8 )
| ( x5 = x6 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1665,plain,
( ( ( x5 = x6 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) )
<=> ( ( x5 = x8 )
| ( x5 = x6 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1666,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x6 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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))) )
| ( x5 = x8 )
| ( x5 = x6 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ) ),
inference(monotonicity,[status(thm)],[1665]) ).
tff(1667,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x6 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),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))) )
| ( x5 = x8 )
| ( x5 = x6 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ) ),
inference(transitivity,[status(thm)],[1666,1664]) ).
tff(1668,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x6 )
| ( x5 = x8 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(1669,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x5 = x8 )
| ( x5 = x6 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[1668,1667]) ).
tff(1670,plain,
( ( x5 = x6 )
| ~ heap(sep(lseg(x5,x8),sep(lseg(x5,x6),sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x7,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))))) ),
inference(unit_resolution,[status(thm)],[1669,184,693]) ).
tff(1671,plain,
x5 = x6,
inference(unit_resolution,[status(thm)],[1670,1663]) ).
tff(1672,plain,
x6 = x5,
inference(symmetry,[status(thm)],[1671]) ).
tff(1673,plain,
x6 = x3,
inference(transitivity,[status(thm)],[1672,612]) ).
tff(1674,plain,
lseg(x6,x8) = lseg(x3,x7),
inference(monotonicity,[status(thm)],[1673,285]) ).
tff(1675,plain,
lseg(x3,x7) = lseg(x6,x8),
inference(symmetry,[status(thm)],[1674]) ).
tff(1676,plain,
lseg(x3,x7) = lseg(x6,x7),
inference(transitivity,[status(thm)],[1675,1617]) ).
tff(1677,plain,
sep(lseg(x3,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))) = sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1676,1608]) ).
tff(1678,plain,
sep(lseg(x6,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x7),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1677]) ).
tff(1679,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))),
inference(symmetry,[status(thm)],[708]) ).
tff(1680,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(transitivity,[status(thm)],[1679,735,1554,729,726,723,658,654,652,643,1678,1615,1600,1597,1577,1565,1576,1580,1569,1562]) ).
tff(1681,plain,
( heap(sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp)))))))))
<=> heap(sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) ),
inference(monotonicity,[status(thm)],[1680]) ).
tff(1682,plain,
( heap(sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))))
<=> heap(sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),sep(lseg(x6,x7),emp))))))))) ),
inference(symmetry,[status(thm)],[1681]) ).
tff(1683,plain,
( heap(sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))))
<=> heap(sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) ),
inference(transitivity,[status(thm)],[1682,1560,706,620,207]) ).
tff(1684,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x5,x5),sep(lseg(x5,x1),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(x5,x1),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(1685,plain,
sep(lseg(x5,x5),sep(lseg(x5,x1),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(x5,x1),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)],[1684,199]) ).
tff(1686,plain,
sep(lseg(x5,x5),sep(lseg(x5,x1),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(x3,x5),sep(lseg(x5,x1),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)],[613]) ).
tff(1687,plain,
sep(lseg(x3,x5),sep(lseg(x5,x1),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(x5,x5),sep(lseg(x5,x1),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(symmetry,[status(thm)],[1686]) ).
tff(1688,plain,
sep(lseg(x3,x5),sep(lseg(x7,x8),sep(lseg(x5,x1),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(x3,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)],[1101]) ).
tff(1689,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = 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(x8,x11),emp))))))),
inference(symmetry,[status(thm)],[1073]) ).
tff(1690,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1064]) ).
tff(1691,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1582]) ).
tff(1692,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))),
inference(transitivity,[status(thm)],[1691,1593]) ).
tff(1693,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp))))))),
inference(monotonicity,[status(thm)],[1692]) ).
tff(1694,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(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1695,plain,
sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1694,7]) ).
tff(1696,plain,
sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1695]) ).
tff(1697,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(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1698,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1697,7]) ).
tff(1699,plain,
sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[210]) ).
tff(1700,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[1699]) ).
tff(1701,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1700]) ).
tff(1702,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[1701,1698]) ).
tff(1703,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x4,x7),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1702]) ).
tff(1704,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = 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(x8,x11),emp))))))),
inference(transitivity,[status(thm)],[1703,1696,1693,1061,1690,1689]) ).
tff(1705,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,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,x12),sep(lseg(x3,x12),sep(lseg(x4,x7),sep(lseg(x6,x9),sep(lseg(x8,x11),emp)))))))),
inference(monotonicity,[status(thm)],[1704]) ).
tff(1706,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(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1707,plain,
sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(unit_resolution,[status(thm)],[1706,7]) ).
tff(1708,plain,
sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x7,x8),sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(symmetry,[status(thm)],[1707]) ).
tff(1709,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(monotonicity,[status(thm)],[1589]) ).
tff(1710,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[1709]) ).
tff(1711,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1712,plain,
sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(unit_resolution,[status(thm)],[1711,7]) ).
tff(1713,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))),
inference(symmetry,[status(thm)],[1712]) ).
tff(1714,plain,
sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))) = sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))),
inference(transitivity,[status(thm)],[1713,1710]) ).
tff(1715,plain,
sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[1714]) ).
tff(1716,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1715]) ).
tff(1717,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1716]) ).
tff(1718,plain,
sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1717]) ).
tff(1719,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1720,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))),
inference(unit_resolution,[status(thm)],[1719,7]) ).
tff(1721,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[212]) ).
tff(1722,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1721]) ).
tff(1723,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(1724,plain,
sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(unit_resolution,[status(thm)],[1723,7]) ).
tff(1725,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1724]) ).
tff(1726,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[1699]) ).
tff(1727,plain,
sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x4,x12),sep(lseg(x3,x5),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(symmetry,[status(thm)],[1726]) ).
tff(1728,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x7,x8),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(monotonicity,[status(thm)],[1714]) ).
tff(1729,plain,
sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp)))))) = sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))),
inference(transitivity,[status(thm)],[1728,1727,1725,1722]) ).
tff(1730,plain,
sep(lseg(x5,x1),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(monotonicity,[status(thm)],[1729]) ).
tff(1731,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,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(x8,x11),sep(lseg(x4,x12),sep(lseg(x6,x9),emp))))))),
inference(symmetry,[status(thm)],[1730]) ).
tff(1732,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))) = sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))),
inference(transitivity,[status(thm)],[1731,1720,1718]) ).
tff(1733,plain,
sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[1732]) ).
tff(1734,plain,
lseg(x4,x8) = lseg(x4,x7),
inference(symmetry,[status(thm)],[1612]) ).
tff(1735,plain,
lseg(x12,x8) = lseg(x4,x8),
inference(monotonicity,[status(thm)],[190]) ).
tff(1736,plain,
lseg(x12,x8) = lseg(x4,x7),
inference(transitivity,[status(thm)],[1735,1734]) ).
tff(1737,plain,
sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x4,x7),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(monotonicity,[status(thm)],[1736]) ).
tff(1738,plain,
sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x5,x1),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(transitivity,[status(thm)],[1737,1733,1708,1705,1077,1688,1687,1685]) ).
tff(1739,plain,
lseg(x1,x12) = lseg(x3,x12),
inference(monotonicity,[status(thm)],[1247]) ).
tff(1740,plain,
lseg(x1,x12) = lseg(x3,x5),
inference(transitivity,[status(thm)],[1739,1553]) ).
tff(1741,plain,
sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1740,1738]) ).
tff(1742,plain,
sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))),
inference(transitivity,[status(thm)],[1741,1101,1078,1075,1052,1049,1569,1562]) ).
tff(1743,plain,
( heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
<=> heap(sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) ),
inference(monotonicity,[status(thm)],[1742]) ).
tff(1744,plain,
sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))) = sep(lseg(x3,x5),sep(lseg(x5,x1),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(transitivity,[status(thm)],[1737,1733,1708,1705,1077,1688]) ).
tff(1745,plain,
sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))) = sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[660,1744]) ).
tff(1746,plain,
lseg(x1,x8) = lseg(x1,x7),
inference(monotonicity,[status(thm)],[285]) ).
tff(1747,plain,
sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))))) = sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1746,1745]) ).
tff(1748,plain,
( heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))))))
<=> heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)],[1747]) ).
tff(1749,plain,
( heap(sep(lseg(x1,x7),sep(lseg(x7,x12),sep(lseg(x3,x5),sep(lseg(x5,x1),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)))))))))))
<=> heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))) ),
inference(symmetry,[status(thm)],[1748]) ).
tff(1750,plain,
heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))),
inference(modus_ponens,[status(thm)],[1540,1749]) ).
tff(1751,plain,
( ( x12 = x8 )
<=> ( x12 = x7 ) ),
inference(monotonicity,[status(thm)],[285]) ).
tff(1752,plain,
( ( x12 = x8 )
<=> ( x7 = x12 ) ),
inference(transitivity,[status(thm)],[1751,275]) ).
tff(1753,plain,
( ( x7 = x12 )
<=> ( x12 = x8 ) ),
inference(symmetry,[status(thm)],[1752]) ).
tff(1754,plain,
( ( x7 != x12 )
<=> ( x12 != x8 ) ),
inference(monotonicity,[status(thm)],[1753]) ).
tff(1755,plain,
x12 != x8,
inference(modus_ponens,[status(thm)],[279,1754]) ).
tff(1756,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)))) )
| ( x12 = x8 )
| heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),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)))) )
| ( x12 = x8 )
| heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1757,plain,
( ( heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ( x12 = x8 )
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))) )
<=> ( ( x12 = x8 )
| heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1758,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,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ( x12 = x8 )
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),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)))) )
| ( x12 = x8 )
| heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))) ) ),
inference(monotonicity,[status(thm)],[1757]) ).
tff(1759,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,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ( x12 = x8 )
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),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)))) )
| ( x12 = x8 )
| heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))) ) ),
inference(transitivity,[status(thm)],[1758,1756]) ).
tff(1760,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,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ( x12 = x8 )
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(1761,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)))) )
| ( x12 = x8 )
| heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[1760,1759]) ).
tff(1762,plain,
( heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))
| ~ heap(sep(lseg(x1,x8),sep(lseg(x8,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))))) ),
inference(unit_resolution,[status(thm)],[1761,590,1755]) ).
tff(1763,plain,
heap(sep(lseg(x1,x12),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x3,x5),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp)))))))))),
inference(unit_resolution,[status(thm)],[1762,1750]) ).
tff(1764,plain,
heap(sep(lseg(x3,x5),sep(lseg(x3,x12),sep(lseg(x7,x8),sep(lseg(x5,x1),sep(lseg(x4,x7),sep(lseg(x4,x12),sep(lseg(x8,x11),sep(lseg(x6,x9),emp))))))))),
inference(modus_ponens,[status(thm)],[1763,1743]) ).
tff(1765,plain,
heap(sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))),
inference(modus_ponens,[status(thm)],[1764,1683]) ).
tff(1766,plain,
( ( x6 = x7 )
<=> ( x3 = x8 ) ),
inference(monotonicity,[status(thm)],[1673,284]) ).
tff(1767,plain,
( ( x3 = x8 )
<=> ( x6 = x7 ) ),
inference(symmetry,[status(thm)],[1766]) ).
tff(1768,plain,
( ( x3 != x8 )
<=> ( x6 != x7 ) ),
inference(monotonicity,[status(thm)],[1767]) ).
tff(1769,plain,
x6 != x7,
inference(modus_ponens,[status(thm)],[603,1768]) ).
tff(1770,plain,
( ( x6 = x9 )
<=> ( x5 = x9 ) ),
inference(monotonicity,[status(thm)],[1672]) ).
tff(1771,plain,
( ( x5 = x9 )
<=> ( x6 = x9 ) ),
inference(symmetry,[status(thm)],[1770]) ).
tff(1772,plain,
( ( x5 != x9 )
<=> ( x6 != x9 ) ),
inference(monotonicity,[status(thm)],[1771]) ).
tff(1773,plain,
( ( x5 != x9 )
<=> ( x5 != x9 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1774,axiom,
x5 != x9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_5) ).
tff(1775,plain,
x5 != x9,
inference(modus_ponens,[status(thm)],[1774,1773]) ).
tff(1776,plain,
x6 != x9,
inference(modus_ponens,[status(thm)],[1775,1772]) ).
tff(1777,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x6 = x7 )
| ( x6 = x9 )
| ~ heap(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))) )
| ( x6 = x7 )
| ( x6 = x9 )
| ~ heap(sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1778,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x6 = x7 )
| ( x6 = x9 )
| ~ heap(sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(1779,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x6 = x7 )
| ( x6 = x9 )
| ~ heap(sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) ),
inference(modus_ponens,[status(thm)],[1778,1777]) ).
tff(1780,plain,
( ( x6 = x7 )
| ( x6 = x9 )
| ~ heap(sep(lseg(x6,x9),sep(lseg(x6,x7),sep(lseg(x8,x11),emp)))) ),
inference(unit_resolution,[status(thm)],[1779,184]) ).
tff(1781,plain,
$false,
inference(unit_resolution,[status(thm)],[1780,1776,1769,1765]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW429-1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 16:34:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 5.62/3.83 % SZS status Unsatisfiable
% 5.62/3.83 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------