TSTP Solution File: SWW427-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW427-1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 0.47s 0.62s
% Output : Proof 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 120
% Syntax : Number of formulae : 576 ( 414 unt; 14 typ; 0 def)
% Number of atoms : 878 ( 747 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 515 ( 203 ~; 255 |; 0 &)
% ( 57 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 419 ( 406 !; 0 ?; 419 :)
% Comments :
%------------------------------------------------------------------------------
tff(x1_type,type,
x1: $i ).
tff(x3_type,type,
x3: $i ).
tff(x11_type,type,
x11: $i ).
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(x5_type,type,
x5: $i ).
tff(x4_type,type,
x4: $i ).
tff(x6_type,type,
x6: $i ).
tff(x7_type,type,
x7: $i ).
tff(x10_type,type,
x10: $i ).
tff(x9_type,type,
x9: $i ).
tff(x2_type,type,
x2: $i ).
tff(1,plain,
( ( x11 = x1 )
<=> ( x1 = x11 ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,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(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(quant_intro,[status(thm)],[2]) ).
tff(4,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(5,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(6,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(skolemize,[status(sab)],[6]) ).
tff(8,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(10,plain,
sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[9,8]) ).
tff(11,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[11,8]) ).
tff(13,plain,
sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[14,10]) ).
tff(16,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[17,8]) ).
tff(19,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(transitivity,[status(thm)],[19,16]) ).
tff(21,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),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(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))),
inference(unit_resolution,[status(thm)],[23,8]) ).
tff(25,plain,
sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[27,8]) ).
tff(29,plain,
sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[29,26]) ).
tff(31,plain,
sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[33,8]) ).
tff(35,plain,
sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(transitivity,[status(thm)],[35,32]) ).
tff(37,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(unit_resolution,[status(thm)],[38,8]) ).
tff(40,plain,
sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[41,8]) ).
tff(43,plain,
sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[30]) ).
tff(44,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[46,8]) ).
tff(48,plain,
sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[48,43]) ).
tff(50,plain,
sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[51,8]) ).
tff(53,plain,
sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(transitivity,[status(thm)],[53,50,45,42]) ).
tff(55,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) = sep(lseg(x9,x2),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) = sep(lseg(x9,x2),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(unit_resolution,[status(thm)],[55,8]) ).
tff(57,plain,
sep(lseg(x9,x2),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[10]) ).
tff(59,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(unit_resolution,[status(thm)],[63,8]) ).
tff(65,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(transitivity,[status(thm)],[65,62]) ).
tff(67,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) = sep(lseg(x9,x2),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) = sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(transitivity,[status(thm)],[67,57]) ).
tff(69,plain,
( heap(sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))))
<=> heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))))
<=> heap(sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))))
<=> heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_10) ).
tff(73,plain,
heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
heap(sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))),
inference(modus_ponens,[status(thm)],[73,70]) ).
tff(75,plain,
( ( x9 = x7 )
<=> ( x7 = x9 ) ),
inference(commutativity,[status(thm)],]) ).
tff(76,plain,
( ( x7 = x9 )
<=> ( x9 = x7 ) ),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ( x7 != x9 )
<=> ( x9 != x7 ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( x7 != x9 )
<=> ( x7 != x9 ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
x7 != x9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_8) ).
tff(80,plain,
x7 != x9,
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
x9 != x7,
inference(modus_ponens,[status(thm)],[80,77]) ).
tff(82,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(83,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)],[82]) ).
tff(84,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(85,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(86,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)],[85]) ).
tff(87,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(88,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)],[87,86]) ).
tff(89,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)],[88,84]) ).
tff(90,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)],[89]) ).
tff(91,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)],[90,83]) ).
tff(92,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x9 = x7 )
| ( x9 = x2 )
| ~ heap(sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x9 = x7 )
| ( x9 = x2 )
| ~ heap(sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x9 = x7 )
| ( x9 = x2 )
| ~ heap(sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x9 = x7 )
| ( x9 = x2 )
| ~ heap(sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ( x9 = x2 )
| ~ heap(sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ),
inference(unit_resolution,[status(thm)],[94,91,81]) ).
tff(96,plain,
x9 = x2,
inference(unit_resolution,[status(thm)],[95,74]) ).
tff(97,plain,
x2 = x9,
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
lseg(x11,x2) = lseg(x11,x9),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(monotonicity,[status(thm)],[98,54]) ).
tff(100,plain,
sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(transitivity,[status(thm)],[99,40,37,22]) ).
tff(101,plain,
( heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))
<=> heap(sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( heap(sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))
<=> heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(unit_resolution,[status(thm)],[103,8]) ).
tff(105,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[105,8]) ).
tff(107,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(transitivity,[status(thm)],[109,104]) ).
tff(111,plain,
lseg(x2,x2) = lseg(x9,x2),
inference(monotonicity,[status(thm)],[97]) ).
tff(112,plain,
lseg(x9,x2) = lseg(x2,x2),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
sep(lseg(x9,x2),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) = sep(lseg(x2,x2),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(monotonicity,[status(thm)],[112,110]) ).
tff(114,plain,
sep(lseg(x2,x2),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) = sep(lseg(x9,x2),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
^ [Sigma: $i,X: $i] :
refl(
( ( sep(lseg(X,X),Sigma) = Sigma )
<=> ( sep(lseg(X,X),Sigma) = Sigma ) )),
inference(bind,[status(th)],]) ).
tff(116,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)],[115]) ).
tff(117,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(118,axiom,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',normalization) ).
tff(119,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
sep(lseg(x2,x2),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(unit_resolution,[status(thm)],[122,121]) ).
tff(124,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x2,x2),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(transitivity,[status(thm)],[21,65,62,109,104,124,114,57]) ).
tff(126,plain,
( heap(sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))
<=> heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))))
<=> heap(sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))))
<=> heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ),
inference(transitivity,[status(thm)],[127,102]) ).
tff(129,plain,
heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(modus_ponens,[status(thm)],[73,128]) ).
tff(130,plain,
( ( x11 = x2 )
<=> ( x2 = x11 ) ),
inference(commutativity,[status(thm)],]) ).
tff(131,plain,
( ( x2 = x11 )
<=> ( x11 = x2 ) ),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ( x2 != x11 )
<=> ( x11 != x2 ) ),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
( ( x2 != x11 )
<=> ( x2 != x11 ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,axiom,
x2 != x11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_9) ).
tff(135,plain,
x2 != x11,
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
x11 != x2,
inference(modus_ponens,[status(thm)],[135,132]) ).
tff(137,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x3 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x3 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x3 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x3 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( ( x11 = x3 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ),
inference(unit_resolution,[status(thm)],[139,91]) ).
tff(141,plain,
x11 = x3,
inference(unit_resolution,[status(thm)],[140,136,129]) ).
tff(142,plain,
x3 = x11,
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( ( x3 = x1 )
<=> ( x11 = x1 ) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ( x3 = x1 )
<=> ( x1 = x11 ) ),
inference(transitivity,[status(thm)],[143,1]) ).
tff(145,plain,
( ( x1 = x11 )
<=> ( x3 = x1 ) ),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ( x1 != x11 )
<=> ( x3 != x1 ) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ( x1 != x11 )
<=> ( x1 != x11 ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,axiom,
x1 != x11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_2) ).
tff(149,plain,
x1 != x11,
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
x3 != x1,
inference(modus_ponens,[status(thm)],[149,146]) ).
tff(151,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))),
inference(unit_resolution,[status(thm)],[151,8]) ).
tff(153,plain,
sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(unit_resolution,[status(thm)],[155,8]) ).
tff(157,plain,
sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))),
inference(transitivity,[status(thm)],[157,154]) ).
tff(159,plain,
sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[163,8]) ).
tff(165,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[165,162]) ).
tff(167,plain,
lseg(x2,x7) = lseg(x9,x7),
inference(monotonicity,[status(thm)],[97]) ).
tff(168,plain,
sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[167,166]) ).
tff(169,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[161,164]) ).
tff(171,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[173,8]) ).
tff(175,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[176,8]) ).
tff(178,plain,
sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[158]) ).
tff(179,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[180,177]) ).
tff(182,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[153]) ).
tff(184,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[185,8]) ).
tff(187,plain,
sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[187,184]) ).
tff(189,plain,
sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[191,8]) ).
tff(193,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[188]) ).
tff(195,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[179]) ).
tff(198,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(200,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[199,8]) ).
tff(201,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(203,plain,
sep(lseg(x2,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[202,121]) ).
tff(204,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[197,200]) ).
tff(205,plain,
sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x2,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[112,204]) ).
tff(206,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(207,plain,
sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[206,8]) ).
tff(208,plain,
sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[208,194]) ).
tff(210,plain,
sep(lseg(x9,x2),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(212,plain,
sep(lseg(x9,x2),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[211,8]) ).
tff(213,plain,
sep(lseg(x11,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x2),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(215,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[214,8]) ).
tff(216,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x3),sep(lseg(x4,x5),sep(lseg(x11,x6),emp))) = sep(lseg(x4,x5),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
sep(lseg(x11,x3),sep(lseg(x4,x5),sep(lseg(x11,x6),emp))) = sep(lseg(x4,x5),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))),
inference(unit_resolution,[status(thm)],[219,8]) ).
tff(221,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x6),sep(lseg(x4,x5),emp)) = sep(lseg(x4,x5),sep(lseg(x11,x6),emp)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(222,plain,
sep(lseg(x11,x6),sep(lseg(x4,x5),emp)) = sep(lseg(x4,x5),sep(lseg(x11,x6),emp)),
inference(unit_resolution,[status(thm)],[221,8]) ).
tff(223,plain,
sep(lseg(x4,x5),sep(lseg(x11,x6),emp)) = sep(lseg(x11,x6),sep(lseg(x4,x5),emp)),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
sep(lseg(x11,x3),sep(lseg(x4,x5),sep(lseg(x11,x6),emp))) = sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x3),sep(lseg(x4,x5),sep(lseg(x11,x6),emp))),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))),
inference(symmetry,[status(thm)],[152]) ).
tff(227,plain,
sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x4,x5),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))),
inference(transitivity,[status(thm)],[226,225,220]) ).
tff(228,plain,
sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))) = sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[228]) ).
tff(230,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))) = sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(231,plain,
sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))) = sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))),
inference(unit_resolution,[status(thm)],[230,8]) ).
tff(232,plain,
sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))) = sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))) = sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(transitivity,[status(thm)],[232,229]) ).
tff(234,plain,
sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),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(x9,x7),sep(lseg(x9,x2),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(239,plain,
sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))),
inference(unit_resolution,[status(thm)],[238,8]) ).
tff(240,plain,
sep(lseg(x9,x2),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[233]) ).
tff(241,plain,
sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x2),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[242,239,237,218]) ).
tff(244,plain,
sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x9),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[243]) ).
tff(245,plain,
sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))) = sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[242]) ).
tff(246,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))) = sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))),
inference(symmetry,[status(thm)],[239]) ).
tff(247,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))) = sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[246,245]) ).
tff(248,plain,
lseg(x3,x2) = lseg(x11,x9),
inference(monotonicity,[status(thm)],[142,97]) ).
tff(249,plain,
sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[248,247]) ).
tff(250,plain,
sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[249,244,213,210,205,203,201,198]) ).
tff(251,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(252,plain,
sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[251,8]) ).
tff(253,plain,
sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[253,159]) ).
tff(255,plain,
sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(257,plain,
sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[256,8]) ).
tff(258,plain,
sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[258,255]) ).
tff(260,plain,
sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(262,plain,
sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[261,8]) ).
tff(263,plain,
sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[262]) ).
tff(264,plain,
sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))),
inference(monotonicity,[status(thm)],[226]) ).
tff(265,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x6),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(266,plain,
sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x6),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(unit_resolution,[status(thm)],[265,8]) ).
tff(267,plain,
sep(lseg(x11,x6),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
sep(lseg(x11,x6),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))),
inference(transitivity,[status(thm)],[267,264]) ).
tff(269,plain,
sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[268]) ).
tff(270,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(271,plain,
sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[270,8]) ).
tff(272,plain,
sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[272,269]) ).
tff(274,plain,
sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[273]) ).
tff(275,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(276,plain,
sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[275,8]) ).
tff(277,plain,
sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x11,x6),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[277,274]) ).
tff(279,plain,
sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(281,plain,
sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[280,8]) ).
tff(282,plain,
sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(transitivity,[status(thm)],[282,279,45,42]) ).
tff(284,plain,
sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(monotonicity,[status(thm)],[98,283]) ).
tff(285,plain,
sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(transitivity,[status(thm)],[284,40,37,65,62,109,104,124,114,57]) ).
tff(286,plain,
( heap(sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))))
<=> heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))))
<=> heap(sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
heap(sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))),
inference(modus_ponens,[status(thm)],[73,287]) ).
tff(289,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x6 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x6 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(290,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x6 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(291,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x6 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ),
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,plain,
( ( x11 = x6 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x6),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ),
inference(unit_resolution,[status(thm)],[291,91,136]) ).
tff(293,plain,
x11 = x6,
inference(unit_resolution,[status(thm)],[292,288]) ).
tff(294,plain,
x6 = x11,
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
x6 = x3,
inference(transitivity,[status(thm)],[294,141]) ).
tff(296,plain,
lseg(x11,x6) = lseg(x11,x3),
inference(monotonicity,[status(thm)],[295]) ).
tff(297,plain,
lseg(x11,x3) = lseg(x11,x6),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[50]) ).
tff(299,plain,
sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[264]) ).
tff(300,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(303,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[302,8]) ).
tff(304,plain,
sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[304,301]) ).
tff(306,plain,
sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(308,plain,
sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[307,8]) ).
tff(309,plain,
sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[309,306]) ).
tff(311,plain,
sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[310]) ).
tff(312,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(313,plain,
sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[312,8]) ).
tff(314,plain,
sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(transitivity,[status(thm)],[314,311,298,52]) ).
tff(316,plain,
sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(monotonicity,[status(thm)],[315]) ).
tff(317,plain,
( heap(sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))))
<=> heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))) ),
inference(monotonicity,[status(thm)],[316]) ).
tff(318,plain,
( heap(sep(lseg(x11,x2),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))
<=> heap(sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ),
inference(symmetry,[status(thm)],[317]) ).
tff(319,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))))
<=> heap(sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ),
inference(transitivity,[status(thm)],[127,102,318]) ).
tff(320,plain,
heap(sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))),
inference(modus_ponens,[status(thm)],[73,319]) ).
tff(321,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(322,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(323,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x11 = x7 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ),
inference(modus_ponens,[status(thm)],[322,321]) ).
tff(324,plain,
( ( x11 = x7 )
| ( x11 = x2 )
| ~ heap(sep(lseg(x11,x2),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x6),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))) ),
inference(unit_resolution,[status(thm)],[323,91]) ).
tff(325,plain,
x11 = x7,
inference(unit_resolution,[status(thm)],[324,136,320]) ).
tff(326,plain,
x7 = x11,
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
x7 = x3,
inference(transitivity,[status(thm)],[326,141]) ).
tff(328,plain,
lseg(x11,x7) = lseg(x11,x3),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
lseg(x11,x7) = lseg(x11,x6),
inference(transitivity,[status(thm)],[328,297]) ).
tff(330,plain,
sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x6),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(332,plain,
sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))),
inference(unit_resolution,[status(thm)],[331,8]) ).
tff(333,plain,
sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))) = sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(monotonicity,[status(thm)],[333]) ).
tff(335,plain,
sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[335]) ).
tff(337,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[336]) ).
tff(338,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(339,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[338,8]) ).
tff(340,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[339]) ).
tff(341,plain,
sep(lseg(x2,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))) = sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))),
inference(monotonicity,[status(thm)],[111]) ).
tff(342,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(343,plain,
sep(lseg(x2,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))),
inference(unit_resolution,[status(thm)],[342,121]) ).
tff(344,plain,
sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))) = sep(lseg(x2,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))) = sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))),
inference(transitivity,[status(thm)],[344,341]) ).
tff(346,plain,
sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))) = sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[345]) ).
tff(347,plain,
sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[347]) ).
tff(349,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[348,340,337]) ).
tff(350,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[349]) ).
tff(351,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(352,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[351,8]) ).
tff(353,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[352]) ).
tff(354,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[347]) ).
tff(355,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(357,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[356,8]) ).
tff(358,plain,
sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(monotonicity,[status(thm)],[333]) ).
tff(359,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[358]) ).
tff(360,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[359]) ).
tff(361,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[360,357,355]) ).
tff(362,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x3),sep(lseg(x4,x5),emp)) = sep(lseg(x4,x5),sep(lseg(x11,x3),emp)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(364,plain,
sep(lseg(x11,x3),sep(lseg(x4,x5),emp)) = sep(lseg(x4,x5),sep(lseg(x11,x3),emp)),
inference(unit_resolution,[status(thm)],[363,8]) ).
tff(365,plain,
sep(lseg(x4,x5),sep(lseg(x11,x3),emp)) = sep(lseg(x11,x3),sep(lseg(x4,x5),emp)),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
sep(lseg(x11,x9),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))) = sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))),
inference(monotonicity,[status(thm)],[365]) ).
tff(367,plain,
sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x9),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))),
inference(symmetry,[status(thm)],[366]) ).
tff(368,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(monotonicity,[status(thm)],[367]) ).
tff(369,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[368]) ).
tff(370,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(371,plain,
sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(unit_resolution,[status(thm)],[370,8]) ).
tff(372,plain,
sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x2,x2),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(374,plain,
sep(lseg(x2,x2),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(unit_resolution,[status(thm)],[373,121]) ).
tff(375,plain,
sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(transitivity,[status(thm)],[372,369]) ).
tff(376,plain,
sep(lseg(x2,x2),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[111,375]) ).
tff(377,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x2,x2),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(transitivity,[status(thm)],[377,374,372,369]) ).
tff(379,plain,
sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[378]) ).
tff(380,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[359]) ).
tff(381,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[380]) ).
tff(382,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(383,plain,
sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[382,8]) ).
tff(384,plain,
sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[383]) ).
tff(385,plain,
sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[384,381]) ).
tff(386,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[385]) ).
tff(387,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[386,379]) ).
tff(388,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(390,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[389,8]) ).
tff(391,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))),
inference(symmetry,[status(thm)],[390]) ).
tff(392,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[385]) ).
tff(393,plain,
sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[392]) ).
tff(394,plain,
sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[378]) ).
tff(395,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[395,393]) ).
tff(397,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x9,x2),sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[396]) ).
tff(398,plain,
sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[375]) ).
tff(399,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(400,plain,
sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(unit_resolution,[status(thm)],[399,8]) ).
tff(401,plain,
sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(symmetry,[status(thm)],[400]) ).
tff(402,plain,
sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[401,398]) ).
tff(403,plain,
sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[402]) ).
tff(404,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(405,plain,
sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(unit_resolution,[status(thm)],[404,8]) ).
tff(406,plain,
sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(symmetry,[status(thm)],[405]) ).
tff(407,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(408,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(unit_resolution,[status(thm)],[407,8]) ).
tff(409,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(symmetry,[status(thm)],[408]) ).
tff(410,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(monotonicity,[status(thm)],[409]) ).
tff(411,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(monotonicity,[status(thm)],[411]) ).
tff(413,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(414,plain,
sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))),
inference(unit_resolution,[status(thm)],[413,8]) ).
tff(415,plain,
sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))),
inference(monotonicity,[status(thm)],[364]) ).
tff(416,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(417,plain,
sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))),
inference(unit_resolution,[status(thm)],[416,8]) ).
tff(418,plain,
sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))) = sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))),
inference(symmetry,[status(thm)],[417]) ).
tff(419,plain,
sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))) = sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))),
inference(transitivity,[status(thm)],[418,415]) ).
tff(420,plain,
sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(monotonicity,[status(thm)],[419]) ).
tff(421,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))),
inference(transitivity,[status(thm)],[421,414]) ).
tff(423,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[422]) ).
tff(424,plain,
sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(symmetry,[status(thm)],[423]) ).
tff(425,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(426,plain,
sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[425,8]) ).
tff(427,plain,
sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))) = sep(lseg(x10,x1),sep(lseg(x11,x3),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(transitivity,[status(thm)],[427,424]) ).
tff(429,plain,
sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x9),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(monotonicity,[status(thm)],[428]) ).
tff(430,plain,
sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[429,412,406,403,397,391,388,362,353,350]) ).
tff(431,plain,
lseg(x11,x3) = lseg(x11,x7),
inference(symmetry,[status(thm)],[328]) ).
tff(432,plain,
sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[431,430]) ).
tff(433,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(434,plain,
sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x3),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[433,8]) ).
tff(435,plain,
sep(lseg(x11,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(monotonicity,[status(thm)],[431,428]) ).
tff(436,plain,
sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x11,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[435]) ).
tff(437,plain,
sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(monotonicity,[status(thm)],[410]) ).
tff(438,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(439,plain,
sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(unit_resolution,[status(thm)],[438,8]) ).
tff(440,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(441,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(unit_resolution,[status(thm)],[440,8]) ).
tff(442,plain,
sep(lseg(x11,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))) = sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))),
inference(monotonicity,[status(thm)],[365]) ).
tff(443,plain,
sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))),
inference(symmetry,[status(thm)],[442]) ).
tff(444,plain,
sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(monotonicity,[status(thm)],[443]) ).
tff(445,plain,
sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[444]) ).
tff(446,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(447,plain,
sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(unit_resolution,[status(thm)],[446,8]) ).
tff(448,plain,
sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(symmetry,[status(thm)],[447]) ).
tff(449,plain,
sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(transitivity,[status(thm)],[448,445]) ).
tff(450,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[449]) ).
tff(451,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),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(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(453,plain,
sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))),
inference(unit_resolution,[status(thm)],[452,8]) ).
tff(454,plain,
sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))) = sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))),
inference(symmetry,[status(thm)],[453]) ).
tff(455,plain,
sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp)))) = sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(monotonicity,[status(thm)],[454]) ).
tff(456,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[455]) ).
tff(457,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(458,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[457,8]) ).
tff(459,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[458]) ).
tff(460,plain,
sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp)))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))),
inference(monotonicity,[status(thm)],[454]) ).
tff(461,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp)))),
inference(symmetry,[status(thm)],[460]) ).
tff(462,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))),
inference(monotonicity,[status(thm)],[461]) ).
tff(463,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(transitivity,[status(thm)],[462,459,456,451,441]) ).
tff(464,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(monotonicity,[status(thm)],[463]) ).
tff(465,plain,
sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[462]) ).
tff(466,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x3),sep(lseg(x11,x7),sep(lseg(x4,x5),emp))))),
inference(symmetry,[status(thm)],[456]) ).
tff(467,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))),
inference(transitivity,[status(thm)],[450,466,458,465]) ).
tff(468,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(monotonicity,[status(thm)],[467]) ).
tff(469,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(470,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(unit_resolution,[status(thm)],[469,8]) ).
tff(471,plain,
sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))) = sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(transitivity,[status(thm)],[444,447]) ).
tff(472,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))) = sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(monotonicity,[status(thm)],[471]) ).
tff(473,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(monotonicity,[status(thm)],[472]) ).
tff(474,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[473,470,468,464,439,437,436]) ).
tff(475,plain,
sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[474]) ).
tff(476,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[473]) ).
tff(477,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(symmetry,[status(thm)],[470]) ).
tff(478,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(symmetry,[status(thm)],[468]) ).
tff(479,plain,
sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[464]) ).
tff(480,plain,
sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(symmetry,[status(thm)],[439]) ).
tff(481,plain,
sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(symmetry,[status(thm)],[437]) ).
tff(482,plain,
lseg(x3,x3) = lseg(x11,x3),
inference(monotonicity,[status(thm)],[142]) ).
tff(483,plain,
lseg(x3,x3) = lseg(x11,x7),
inference(transitivity,[status(thm)],[482,431]) ).
tff(484,plain,
sep(lseg(x3,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))),
inference(monotonicity,[status(thm)],[483,428]) ).
tff(485,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(486,plain,
sep(lseg(x3,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))),
inference(unit_resolution,[status(thm)],[485,121]) ).
tff(487,plain,
sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp))))) = sep(lseg(x3,x3),sep(lseg(x11,x3),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[486]) ).
tff(488,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))) = sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(489,plain,
sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))) = sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))),
inference(unit_resolution,[status(thm)],[488,8]) ).
tff(490,plain,
sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))) = sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))),
inference(symmetry,[status(thm)],[489]) ).
tff(491,plain,
sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp)))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(monotonicity,[status(thm)],[490]) ).
tff(492,plain,
sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(transitivity,[status(thm)],[491,409]) ).
tff(493,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(monotonicity,[status(thm)],[492]) ).
tff(494,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(495,plain,
sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))))),
inference(unit_resolution,[status(thm)],[494,8]) ).
tff(496,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))))),
inference(symmetry,[status(thm)],[495]) ).
tff(497,plain,
sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp)))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(monotonicity,[status(thm)],[490]) ).
tff(498,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp)))),
inference(symmetry,[status(thm)],[497]) ).
tff(499,plain,
sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x9,x7),sep(lseg(x11,x3),emp))))),
inference(monotonicity,[status(thm)],[498]) ).
tff(500,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(501,plain,
sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(unit_resolution,[status(thm)],[500,8]) ).
tff(502,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))) = sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
lseg(x7,x10) = lseg(x11,x10),
inference(monotonicity,[status(thm)],[326]) ).
tff(504,plain,
lseg(x11,x10) = lseg(x7,x10),
inference(symmetry,[status(thm)],[503]) ).
tff(505,plain,
lseg(x3,x10) = lseg(x11,x10),
inference(monotonicity,[status(thm)],[142]) ).
tff(506,plain,
lseg(x3,x10) = lseg(x7,x10),
inference(transitivity,[status(thm)],[505,504]) ).
tff(507,plain,
sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))),
inference(monotonicity,[status(thm)],[506,502]) ).
tff(508,plain,
sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))) = sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[507,499,496,493,423,426,487,484,481,480,479,478,477,476]) ).
tff(509,plain,
sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[248,508]) ).
tff(510,plain,
sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))) = sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(transitivity,[status(thm)],[509,475,434,432,330,263,260,169]) ).
tff(511,plain,
( heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp)))))))
<=> heap(sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))) ),
inference(monotonicity,[status(thm)],[510]) ).
tff(512,plain,
( heap(sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))
<=> heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) ),
inference(symmetry,[status(thm)],[511]) ).
tff(513,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(514,plain,
sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[513,8]) ).
tff(515,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(516,plain,
sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(unit_resolution,[status(thm)],[515,8]) ).
tff(517,plain,
sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(symmetry,[status(thm)],[14]) ).
tff(518,plain,
sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))) = sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))),
inference(transitivity,[status(thm)],[58,517,516]) ).
tff(519,plain,
sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x11,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[518]) ).
tff(520,plain,
sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(transitivity,[status(thm)],[519,514]) ).
tff(521,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(monotonicity,[status(thm)],[520]) ).
tff(522,plain,
sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x9),sep(lseg(x7,x10),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(symmetry,[status(thm)],[521]) ).
tff(523,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(524,plain,
sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(unit_resolution,[status(thm)],[523,8]) ).
tff(525,plain,
sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x9,x7),sep(lseg(x11,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(symmetry,[status(thm)],[524]) ).
tff(526,plain,
sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(transitivity,[status(thm)],[171,174]) ).
tff(527,plain,
lseg(x11,x3) = lseg(x3,x3),
inference(symmetry,[status(thm)],[482]) ).
tff(528,plain,
lseg(x11,x7) = lseg(x3,x3),
inference(transitivity,[status(thm)],[328,527]) ).
tff(529,plain,
sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x3,x3),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))),
inference(monotonicity,[status(thm)],[528,526]) ).
tff(530,plain,
sep(lseg(x3,x3),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x11,x7),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(532,plain,
sep(lseg(x3,x3),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))) = sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(unit_resolution,[status(thm)],[531,121]) ).
tff(533,plain,
sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x3,x3),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))),
inference(symmetry,[status(thm)],[532]) ).
tff(534,plain,
sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))) = sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))),
inference(transitivity,[status(thm)],[168,171,174,533,530,525,522,65,62,109,104,124,114,57]) ).
tff(535,plain,
( heap(sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))
<=> heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp)))))))))) ),
inference(monotonicity,[status(thm)],[534]) ).
tff(536,plain,
( heap(sep(lseg(x10,x1),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x7,x10),sep(lseg(x11,x9),sep(lseg(x11,x7),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))))))
<=> heap(sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))) ),
inference(symmetry,[status(thm)],[535]) ).
tff(537,plain,
heap(sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))),
inference(modus_ponens,[status(thm)],[73,536]) ).
tff(538,plain,
heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))),
inference(modus_ponens,[status(thm)],[537,512]) ).
tff(539,plain,
( ( x3 = x2 )
<=> ( x11 = x2 ) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(540,plain,
( ( x3 = x2 )
<=> ( x2 = x11 ) ),
inference(transitivity,[status(thm)],[539,130]) ).
tff(541,plain,
( ( x2 = x11 )
<=> ( x3 = x2 ) ),
inference(symmetry,[status(thm)],[540]) ).
tff(542,plain,
( ( x2 != x11 )
<=> ( x3 != x2 ) ),
inference(monotonicity,[status(thm)],[541]) ).
tff(543,plain,
x3 != x2,
inference(modus_ponens,[status(thm)],[135,542]) ).
tff(544,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x2 )
| ( x3 = x10 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x2 )
| ( x3 = x10 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(545,plain,
( ( ( x3 = x10 )
| ( x3 = x2 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) )
<=> ( ( x3 = x2 )
| ( x3 = x10 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(546,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x10 )
| ( x3 = x2 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x2 )
| ( x3 = x10 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) ) ),
inference(monotonicity,[status(thm)],[545]) ).
tff(547,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x10 )
| ( x3 = x2 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x2 )
| ( x3 = x10 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) ) ),
inference(transitivity,[status(thm)],[546,544]) ).
tff(548,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x10 )
| ( x3 = x2 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(549,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x2 )
| ( x3 = x10 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) ),
inference(modus_ponens,[status(thm)],[548,547]) ).
tff(550,plain,
( ( x3 = x2 )
| ( x3 = x10 )
| ~ heap(sep(lseg(x3,x2),sep(lseg(x3,x10),sep(lseg(x9,x7),sep(lseg(x10,x1),sep(lseg(x4,x5),sep(lseg(x11,x3),emp))))))) ),
inference(unit_resolution,[status(thm)],[549,91]) ).
tff(551,plain,
x3 = x10,
inference(unit_resolution,[status(thm)],[550,543,538]) ).
tff(552,plain,
lseg(x3,x1) = lseg(x10,x1),
inference(monotonicity,[status(thm)],[551]) ).
tff(553,plain,
sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))))) = sep(lseg(x10,x1),sep(lseg(x7,x10),sep(lseg(x9,x7),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x11,x6),sep(lseg(x4,x5),emp))))))),
inference(monotonicity,[status(thm)],[552,250]) ).
tff(554,plain,
sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))))) = sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))),
inference(transitivity,[status(thm)],[553,196,193,190,182,175,172,169]) ).
tff(555,plain,
( heap(sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp)))))))))
<=> heap(sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp)))))))) ),
inference(monotonicity,[status(thm)],[554]) ).
tff(556,plain,
( heap(sep(lseg(x2,x7),sep(lseg(x7,x10),sep(lseg(x10,x1),sep(lseg(x11,x6),sep(lseg(x11,x9),sep(lseg(x11,x3),sep(lseg(x4,x5),emp))))))))
<=> heap(sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))))))) ),
inference(symmetry,[status(thm)],[555]) ).
tff(557,plain,
heap(sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))))))),
inference(modus_ponens,[status(thm)],[537,556]) ).
tff(558,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x2 )
| ( x3 = x1 )
| ~ heap(sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x2 )
| ( x3 = x1 )
| ~ heap(sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(559,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x2 )
| ( x3 = x1 )
| ~ heap(sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(560,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x2 )
| ( x3 = x1 )
| ~ heap(sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))))))) ),
inference(modus_ponens,[status(thm)],[559,558]) ).
tff(561,plain,
( ( x3 = x1 )
| ~ heap(sep(lseg(x3,x1),sep(lseg(x3,x2),sep(lseg(x9,x2),sep(lseg(x9,x7),sep(lseg(x4,x5),sep(lseg(x7,x10),sep(lseg(x11,x3),sep(lseg(x11,x6),emp))))))))) ),
inference(unit_resolution,[status(thm)],[560,91,543]) ).
tff(562,plain,
$false,
inference(unit_resolution,[status(thm)],[561,557,150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW427-1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 16:39:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.47/0.62 % SZS status Unsatisfiable
% 0.47/0.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------