%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW437-1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:37:00 AM UTC 2025
% Result : Unsatisfiable 1.25s 1.44s
% Output : Proof 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 70
% Syntax : Number of formulae : 321 ( 228 unt; 0 typ; 0 def)
% Number of atoms : 550 ( 458 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 366 ( 141 ~; 186 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 310 ( 297 !; 0 ?; 310 :)
% Comments :
%------------------------------------------------------------------------------
tff(heap_type,type,
heap: $i > $o ).
tff(sep_type,type,
sep: ( $i * $i ) > $i ).
tff(emp_type,type,
emp: $i ).
tff(lseg_type,type,
lseg: ( $i * $i ) > $i ).
tff(x8_type,type,
x8: $i ).
tff(x11_type,type,
x11: $i ).
tff(x16_type,type,
x16: $i ).
tff(x3_type,type,
x3: $i ).
tff(x12_type,type,
x12: $i ).
tff(x1_type,type,
x1: $i ).
tff(x7_type,type,
x7: $i ).
tff(x15_type,type,
x15: $i ).
tff(x10_type,type,
x10: $i ).
tff(x5_type,type,
x5: $i ).
tff(x6_type,type,
x6: $i ).
tff(x2_type,type,
x2: $i ).
tff(1,plain,
^ [Sigma: $i,S: $i,T: $i] :
refl(( ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',associative_commutative) ).
tff(5,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(unit_resolution,[status(thm)],[16,7]) ).
tff(18,plain,
sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(unit_resolution,[status(thm)],[19,7]) ).
tff(21,plain,
sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(transitivity,[status(thm)],[27,23]) ).
tff(29,plain,
sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[31,7]) ).
tff(33,plain,
sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(transitivity,[status(thm)],[33,30]) ).
tff(35,plain,
sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(unit_resolution,[status(thm)],[36,7]) ).
tff(38,plain,
sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[39,7]) ).
tff(41,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(unit_resolution,[status(thm)],[43,7]) ).
tff(45,plain,
sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(transitivity,[status(thm)],[45,42]) ).
tff(47,plain,
sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(unit_resolution,[status(thm)],[48,7]) ).
tff(50,plain,
sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(unit_resolution,[status(thm)],[51,7]) ).
tff(53,plain,
sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(symmetry,[status(thm)],[25]) ).
tff(54,plain,
sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(transitivity,[status(thm)],[56,52]) ).
tff(58,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[60,7]) ).
tff(62,plain,
sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(transitivity,[status(thm)],[62,59]) ).
tff(64,plain,
sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(unit_resolution,[status(thm)],[65,7]) ).
tff(67,plain,
sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(transitivity,[status(thm)],[67,64]) ).
tff(69,plain,
sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(transitivity,[status(thm)],[69,50,47,10]) ).
tff(71,plain,
( heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))))
<=> heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_27) ).
tff(75,plain,
heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))),
inference(modus_ponens,[status(thm)],[75,72]) ).
tff(77,plain,
( ( x16 = x7 )
<=> ( x7 = x16 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(78,plain,
( ( x7 = x16 )
<=> ( x16 = x7 ) ),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( ( x7 != x16 )
<=> ( x16 != x7 ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( x7 != x16 )
<=> ( x7 != x16 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
x7 != x16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_10) ).
tff(82,plain,
x7 != x16,
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
x16 != x7,
inference(modus_ponens,[status(thm)],[82,79]) ).
tff(84,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(85,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)],[84]) ).
tff(86,plain,
( ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
<=> ! [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(87,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(88,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)],[87]) ).
tff(89,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(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(modus_ponens,[status(thm)],[89,88]) ).
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)],[90,86]) ).
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))) ),
inference(skolemize,[status(sab)],[91]) ).
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))) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
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))) )
| ( x16 = x7 )
| ( x16 = x3 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x16 = x7 )
| ( x16 = x3 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ( x16 = x3 )
| ( x16 = x7 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) )
<=> ( ( x16 = x7 )
| ( x16 = x3 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x16 = x3 )
| ( x16 = x7 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x16 = x7 )
| ( x16 = x3 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x16 = x3 )
| ( x16 = x7 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x16 = x7 )
| ( x16 = x3 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x16 = x3 )
| ( x16 = x7 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x16 = x7 )
| ( x16 = x3 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ( x16 = x3 )
| ~ heap(sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ),
inference(unit_resolution,[status(thm)],[99,93,83]) ).
tff(101,plain,
x16 = x3,
inference(unit_resolution,[status(thm)],[100,76]) ).
tff(102,plain,
lseg(x16,x3) = lseg(x3,x3),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
lseg(x3,x3) = lseg(x16,x3),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
sep(lseg(x3,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
^ [Sigma: $i,X: $i] :
refl(( ( sep(lseg(X,X),Sigma) = Sigma )
<=> ( sep(lseg(X,X),Sigma) = Sigma ) )),
inference(bind,[status(th)],[]) ).
tff(106,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)],[105]) ).
tff(107,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(108,axiom,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax',normalization) ).
tff(109,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
sep(lseg(x3,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x3,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[115,7]) ).
tff(117,plain,
sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(symmetry,[status(thm)],[26]) ).
tff(118,plain,
sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(transitivity,[status(thm)],[21,117]) ).
tff(119,plain,
sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[26]) ).
tff(123,plain,
sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(unit_resolution,[status(thm)],[124,7]) ).
tff(126,plain,
sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) = sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) = sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))),
inference(unit_resolution,[status(thm)],[127,7]) ).
tff(129,plain,
sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) = sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(transitivity,[status(thm)],[53,131]) ).
tff(133,plain,
sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(unit_resolution,[status(thm)],[135,7]) ).
tff(137,plain,
sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(transitivity,[status(thm)],[137,134]) ).
tff(139,plain,
sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(transitivity,[status(thm)],[139,126,123]) ).
tff(141,plain,
sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[142,7]) ).
tff(144,plain,
sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
sep(lseg(x5,x1),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[138]) ).
tff(146,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(unit_resolution,[status(thm)],[148,7]) ).
tff(150,plain,
sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))) = sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))) = sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))),
inference(unit_resolution,[status(thm)],[151,7]) ).
tff(153,plain,
sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))) = sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) = sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))) = sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))) = sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(transitivity,[status(thm)],[156,150,130,25]) ).
tff(158,plain,
sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))) = sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))) = sep(lseg(x7,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))) = sep(lseg(x7,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))),
inference(unit_resolution,[status(thm)],[159,7]) ).
tff(161,plain,
sep(lseg(x7,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))) = sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
sep(lseg(x7,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))) = sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(transitivity,[status(thm)],[161,158]) ).
tff(163,plain,
sep(lseg(x5,x1),sep(lseg(x7,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x7,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
sep(lseg(x5,x1),sep(lseg(x7,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))),
inference(unit_resolution,[status(thm)],[164,7]) ).
tff(166,plain,
sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(transitivity,[status(thm)],[166,163]) ).
tff(168,plain,
lseg(x16,x7) = lseg(x3,x7),
inference(monotonicity,[status(thm)],[101]) ).
tff(169,plain,
lseg(x3,x7) = lseg(x16,x7),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
sep(lseg(x3,x7),sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[169,167]) ).
tff(171,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x7,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[163]) ).
tff(172,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(unit_resolution,[status(thm)],[172,7]) ).
tff(174,plain,
sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))),
inference(transitivity,[status(thm)],[174,171,165]) ).
tff(176,plain,
sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(transitivity,[status(thm)],[176,170,147,144,141,121,116,114,104,38,35,18,15]) ).
tff(178,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
sep(lseg(x12,x8),sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[178,7]) ).
tff(180,plain,
sep(lseg(x12,x8),sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[167]) ).
tff(181,plain,
sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[174]) ).
tff(183,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[183,7]) ).
tff(185,plain,
sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(unit_resolution,[status(thm)],[186,7]) ).
tff(188,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x15),sep(lseg(x3,x12),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x3,x12),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
sep(lseg(x10,x15),sep(lseg(x3,x12),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x3,x12),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(unit_resolution,[status(thm)],[188,7]) ).
tff(190,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))) = sep(lseg(x3,x12),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(191,plain,
sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))) = sep(lseg(x3,x12),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))),
inference(unit_resolution,[status(thm)],[190,7]) ).
tff(192,plain,
sep(lseg(x3,x12),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))) = sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) = sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) = sep(lseg(x3,x12),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) = sep(lseg(x3,x12),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))),
inference(unit_resolution,[status(thm)],[194,7]) ).
tff(196,plain,
sep(lseg(x3,x12),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) = sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
sep(lseg(x3,x12),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))) = sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))),
inference(transitivity,[status(thm)],[196,193]) ).
tff(198,plain,
sep(lseg(x10,x15),sep(lseg(x3,x12),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(monotonicity,[status(thm)],[197]) ).
tff(199,plain,
sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x10,x15),sep(lseg(x3,x12),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))) = sep(lseg(x3,x12),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))),
inference(transitivity,[status(thm)],[53,199,189]) ).
tff(201,plain,
sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x12,x8),sep(lseg(x3,x12),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
sep(lseg(x12,x8),sep(lseg(x3,x12),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x3,x12),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x3,x12),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
sep(lseg(x12,x8),sep(lseg(x3,x12),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x3,x12),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(unit_resolution,[status(thm)],[203,7]) ).
tff(205,plain,
sep(lseg(x3,x12),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x12,x8),sep(lseg(x3,x12),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(symmetry,[status(thm)],[204]) ).
tff(206,plain,
sep(lseg(x3,x12),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))) = sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))),
inference(transitivity,[status(thm)],[205,202]) ).
tff(207,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(unit_resolution,[status(thm)],[208,7]) ).
tff(210,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x5,x1),sep(lseg(x3,x12),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(transitivity,[status(thm)],[210,207,187]) ).
tff(212,plain,
sep(lseg(x2,x6),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
sep(lseg(x2,x6),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[213,7]) ).
tff(215,plain,
sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x3,x12),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))),
inference(transitivity,[status(thm)],[215,212,185,182,181,179]) ).
tff(217,plain,
sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x3,x7),sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))))) ),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(transitivity,[status(thm)],[18,15]) ).
tff(221,plain,
sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(unit_resolution,[status(thm)],[222,7]) ).
tff(224,plain,
sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(226,plain,
sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(unit_resolution,[status(thm)],[225,7]) ).
tff(227,plain,
sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[12]) ).
tff(228,plain,
sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[227]) ).
tff(230,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(231,plain,
sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[230,7]) ).
tff(232,plain,
sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(transitivity,[status(thm)],[232,229]) ).
tff(234,plain,
sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(unit_resolution,[status(thm)],[235,7]) ).
tff(237,plain,
sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(transitivity,[status(thm)],[237,234,228,226]) ).
tff(239,plain,
sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x16,x3),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(unit_resolution,[status(thm)],[240,7]) ).
tff(242,plain,
sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x2,x6),sep(lseg(x16,x3),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[26]) ).
tff(244,plain,
sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(246,plain,
sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(unit_resolution,[status(thm)],[245,7]) ).
tff(247,plain,
sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(transitivity,[status(thm)],[247,244]) ).
tff(249,plain,
sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(unit_resolution,[status(thm)],[253,7]) ).
tff(255,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(transitivity,[status(thm)],[255,252]) ).
tff(257,plain,
sep(lseg(x3,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x16,x3),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(monotonicity,[status(thm)],[103,256]) ).
tff(258,plain,
( ~ ! [Sigma: $i,X: $i] : ( sep(lseg(X,X),Sigma) = Sigma )
| ( sep(lseg(x3,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(259,plain,
sep(lseg(x3,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(unit_resolution,[status(thm)],[258,111]) ).
tff(260,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x3,x3),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[248]) ).
tff(262,plain,
sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(265,plain,
sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[264,7]) ).
tff(266,plain,
sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[265]) ).
tff(267,plain,
sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(transitivity,[status(thm)],[266,261]) ).
tff(268,plain,
sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x16,x7),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(270,plain,
sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(unit_resolution,[status(thm)],[269,7]) ).
tff(271,plain,
sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x16,x7),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(273,plain,
sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(unit_resolution,[status(thm)],[272,7]) ).
tff(274,plain,
sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(monotonicity,[status(thm)],[138]) ).
tff(278,plain,
sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))) = sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(unit_resolution,[status(thm)],[281,7]) ).
tff(283,plain,
sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x10,x15),sep(lseg(x2,x6),sep(lseg(x7,x1),sep(lseg(x10,x5),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(monotonicity,[status(thm)],[146]) ).
tff(284,plain,
sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(transitivity,[status(thm)],[283,282,280,276]) ).
tff(285,plain,
sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x7),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x12,x8),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[284]) ).
tff(286,plain,
sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x7,x1),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))),
inference(symmetry,[status(thm)],[179]) ).
tff(287,plain,
sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))),
inference(transitivity,[status(thm)],[286,180]) ).
tff(288,plain,
sep(lseg(x3,x7),sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x16,x7),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))),
inference(monotonicity,[status(thm)],[169,287]) ).
tff(289,plain,
sep(lseg(x3,x7),sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(transitivity,[status(thm)],[288,285,271,268,263,260,257,242,239,224,221,10]) ).
tff(290,plain,
( heap(sep(lseg(x3,x7),sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp)))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[289]) ).
tff(291,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x7,x1),sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x3,x16),sep(lseg(x3,x12),sep(lseg(x11,x8),emp))))))))))) ),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))))
<=> heap(sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ),
inference(transitivity,[status(thm)],[291,219]) ).
tff(293,plain,
heap(sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(modus_ponens,[status(thm)],[75,292]) ).
tff(294,plain,
x3 = x16,
inference(symmetry,[status(thm)],[101]) ).
tff(295,plain,
( ( x3 = x7 )
<=> ( x16 = x7 ) ),
inference(monotonicity,[status(thm)],[294]) ).
tff(296,plain,
( ( x3 = x7 )
<=> ( x7 = x16 ) ),
inference(transitivity,[status(thm)],[295,77]) ).
tff(297,plain,
( ( x7 = x16 )
<=> ( x3 = x7 ) ),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
( ( x7 != x16 )
<=> ( x3 != x7 ) ),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
x3 != x7,
inference(modus_ponens,[status(thm)],[82,298]) ).
tff(300,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x12 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x12 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(301,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x12 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x12 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[301,300]) ).
tff(303,plain,
( ( x3 = x12 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x7),sep(lseg(x3,x12),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ),
inference(unit_resolution,[status(thm)],[302,93]) ).
tff(304,plain,
x3 = x12,
inference(unit_resolution,[status(thm)],[303,299,293]) ).
tff(305,plain,
lseg(x3,x8) = lseg(x12,x8),
inference(monotonicity,[status(thm)],[304]) ).
tff(306,plain,
sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x12,x8),sep(lseg(x5,x1),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(monotonicity,[status(thm)],[305,177]) ).
tff(307,plain,
sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))) = sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(transitivity,[status(thm)],[306,10]) ).
tff(308,plain,
( heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))
<=> heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp)))))))))))) ),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
( heap(sep(lseg(x5,x1),sep(lseg(x12,x8),sep(lseg(x2,x6),sep(lseg(x16,x7),sep(lseg(x16,x3),sep(lseg(x10,x15),sep(lseg(x10,x5),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))))
<=> heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ),
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(modus_ponens,[status(thm)],[75,309]) ).
tff(311,plain,
( ( x3 != x8 )
<=> ( x3 != x8 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(312,axiom,
x3 != x8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_6) ).
tff(313,plain,
x3 != x8,
inference(modus_ponens,[status(thm)],[312,311]) ).
tff(314,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(315,plain,
( ( ( x3 = x7 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) )
<=> ( ( x3 = x8 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(316,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x7 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ) ),
inference(monotonicity,[status(thm)],[315]) ).
tff(317,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x7 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ) ),
inference(transitivity,[status(thm)],[316,314]) ).
tff(318,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x7 )
| ( x3 = x8 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(319,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( X = Y )
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) )
| ( x3 = x8 )
| ( x3 = x7 )
| ~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))) ),
inference(modus_ponens,[status(thm)],[318,317]) ).
tff(320,plain,
~ heap(sep(lseg(x3,x8),sep(lseg(x3,x7),sep(lseg(x2,x6),sep(lseg(x5,x1),sep(lseg(x10,x5),sep(lseg(x10,x15),sep(lseg(x7,x1),sep(lseg(x3,x12),sep(lseg(x3,x16),sep(lseg(x11,x8),emp))))))))))),
inference(unit_resolution,[status(thm)],[319,93,313,299]) ).
tff(321,plain,
$false,
inference(unit_resolution,[status(thm)],[320,310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW437-1 : TPTP v9.0.0. Released v5.2.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.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 : Fri Jun 20 11:42:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.25/1.44 % SZS status Unsatisfiable
% 1.25/1.44 % SZS output start Proof
% See solution above
% 1.38/1.53 % E exiting
%------------------------------------------------------------------------------