%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC164-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:30:22 AM UTC 2025
% Result : Unsatisfiable 4.98s 5.16s
% Output : Proof 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 145
% Syntax : Number of formulae : 394 ( 107 unt; 0 typ; 0 def)
% Number of atoms : 2460 ( 745 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 3623 (1686 ~;1708 |; 0 &)
% ( 229 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 129 ( 129 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 675 ( 610 !; 0 ?; 675 :)
% Comments :
%------------------------------------------------------------------------------
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(hd_type,type,
hd: $i > $i ).
tff(sk9_type,type,
sk9: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(1,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(3,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(10,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(16,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssList(cons(sk6,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssList(cons(sk6,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssList(cons(sk6,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssList(cons(sk6,nil)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
ssList(cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[19,16,13,3]) ).
tff(21,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(23,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[26,16,13,23]) ).
tff(28,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(30,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(37,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) )
<=> ( ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))),
inference(unit_resolution,[status(thm)],[46,40,30,27,20]) ).
tff(48,plain,
app(sk7,app(cons(sk5,nil),cons(sk6,nil))) = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
<=> ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
<=> ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))) ),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(57,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ssList(app(sk7,cons(sk5,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk7) )
<=> ( ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk7) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk7) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ssList(app(sk7,cons(sk5,nil))) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
ssList(app(sk7,cons(sk5,nil))),
inference(unit_resolution,[status(thm)],[66,60,30,27]) ).
tff(68,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(sk7,cons(sk5,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(sk7,cons(sk5,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(sk7,cons(sk5,nil))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(sk7,cons(sk5,nil))) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))),
inference(unit_resolution,[status(thm)],[70,60,20,67]) ).
tff(72,plain,
ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),
inference(modus_ponens,[status(thm)],[71,50]) ).
tff(73,plain,
( ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
<=> ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(74,plain,
( ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
<=> ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) ) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(75,plain,
( ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
<=> ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = nil ) ),
inference(transitivity,[status(thm)],[74,73]) ).
tff(76,plain,
( ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = nil )
<=> ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
<=> ( nil != app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( nil = cons(sk6,nil) )
<=> ( cons(sk6,nil) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(79,plain,
( ( cons(sk6,nil) = nil )
<=> ( nil = cons(sk6,nil) ) ),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ( cons(sk6,nil) != nil )
<=> ( nil != cons(sk6,nil) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( cons(U,V) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(87,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( cons(sk6,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( cons(sk6,nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( cons(sk6,nil) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( cons(sk6,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
cons(sk6,nil) != nil,
inference(unit_resolution,[status(thm)],[93,16,90,3]) ).
tff(95,plain,
nil != cons(sk6,nil),
inference(modus_ponens,[status(thm)],[94,80]) ).
tff(96,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).
tff(102,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) )
<=> ( ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ) ),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
( ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ),
inference(unit_resolution,[status(thm)],[111,105,20,67]) ).
tff(113,plain,
app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil,
inference(unit_resolution,[status(thm)],[112,95]) ).
tff(114,plain,
nil != app(sk7,app(cons(sk5,nil),cons(sk6,nil))),
inference(modus_ponens,[status(thm)],[113,77]) ).
tff(115,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
tff(121,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
| ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
| ( cons(hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
| ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
| ( cons(hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
| ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
| ( cons(hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
| ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
| ( cons(hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
( ~ ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
| ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
| ( cons(hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) ) ),
inference(unit_resolution,[status(thm)],[127,124]) ).
tff(129,plain,
cons(hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) = app(sk7,app(cons(sk5,nil),cons(sk6,nil))),
inference(unit_resolution,[status(thm)],[128,114,72]) ).
tff(130,plain,
tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))) = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))),
inference(monotonicity,[status(thm)],[48]) ).
tff(131,plain,
tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))) = hd(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))),
inference(monotonicity,[status(thm)],[48]) ).
tff(133,plain,
hd(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
( ( nil = app(sk7,cons(sk5,nil)) )
<=> ( app(sk7,cons(sk5,nil)) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(135,plain,
( ( app(sk7,cons(sk5,nil)) = nil )
<=> ( nil = app(sk7,cons(sk5,nil)) ) ),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( ( app(sk7,cons(sk5,nil)) != nil )
<=> ( nil != app(sk7,cons(sk5,nil)) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ( nil = cons(sk5,nil) )
<=> ( cons(sk5,nil) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(138,plain,
( ( cons(sk5,nil) = nil )
<=> ( nil = cons(sk5,nil) ) ),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ( cons(sk5,nil) != nil )
<=> ( nil != cons(sk5,nil) ) ),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
cons(sk5,nil) != nil,
inference(unit_resolution,[status(thm)],[142,16,90,23]) ).
tff(144,plain,
nil != cons(sk5,nil),
inference(modus_ponens,[status(thm)],[143,139]) ).
tff(145,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ( app(sk7,cons(sk5,nil)) != nil )
| ( nil = cons(sk5,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ( app(sk7,cons(sk5,nil)) != nil )
| ( nil = cons(sk5,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ( app(sk7,cons(sk5,nil)) != nil )
| ( nil = cons(sk5,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ( app(sk7,cons(sk5,nil)) != nil )
| ( nil = cons(sk5,nil) ) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
( ( app(sk7,cons(sk5,nil)) != nil )
| ( nil = cons(sk5,nil) ) ),
inference(unit_resolution,[status(thm)],[147,105,30,27]) ).
tff(149,plain,
app(sk7,cons(sk5,nil)) != nil,
inference(unit_resolution,[status(thm)],[148,144]) ).
tff(150,plain,
nil != app(sk7,cons(sk5,nil)),
inference(modus_ponens,[status(thm)],[149,136]) ).
tff(151,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(152,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) ),
inference(quant_intro,[status(thm)],[151]) ).
tff(153,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(155,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause123) ).
tff(157,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
inference(modus_ponens,[status(thm)],[157,153]) ).
tff(159,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
inference(skolemize,[status(sab)],[158]) ).
tff(160,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
inference(modus_ponens,[status(thm)],[159,152]) ).
tff(161,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( hd(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = hd(app(sk7,cons(sk5,nil))) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( hd(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = hd(app(sk7,cons(sk5,nil))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( hd(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = hd(app(sk7,cons(sk5,nil))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( hd(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = hd(app(sk7,cons(sk5,nil))) ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
( ( nil = app(sk7,cons(sk5,nil)) )
| ( hd(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = hd(app(sk7,cons(sk5,nil))) ) ),
inference(unit_resolution,[status(thm)],[163,160,20,67]) ).
tff(165,plain,
hd(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = hd(app(sk7,cons(sk5,nil))),
inference(unit_resolution,[status(thm)],[164,150]) ).
tff(166,plain,
hd(app(sk7,cons(sk5,nil))) = hd(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
hd(app(sk7,cons(sk5,nil))) = hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),
inference(transitivity,[status(thm)],[166,133]) ).
tff(168,plain,
cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))) = cons(hd(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))),
inference(monotonicity,[status(thm)],[167,131]) ).
tff(169,plain,
cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))) = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),
inference(transitivity,[status(thm)],[168,129,48]) ).
tff(170,plain,
( ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1 )
<=> ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(172,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
sk1 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(symmetry,[status(thm)],[172]) ).
tff(174,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(176,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(179,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk3,
inference(transitivity,[status(thm)],[172,176]) ).
tff(180,plain,
( ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[180,178]) ).
tff(182,plain,
( ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
( ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = nil )
<=> ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) ) ),
inference(symmetry,[status(thm)],[73]) ).
tff(184,plain,
( ( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) != nil )
<=> ( nil != app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) ) ),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
nil != app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),
inference(modus_ponens,[status(thm)],[113,184]) ).
tff(186,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,axiom,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(188,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(190,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[189]) ).
tff(191,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(193,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[192]) ).
tff(194,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
tff(195,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[195,191]) ).
tff(197,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(skolemize,[status(sab)],[196]) ).
tff(198,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[197,190]) ).
tff(199,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(200,plain,
( ( ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) ) ),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) ) ),
inference(transitivity,[status(thm)],[201,199]) ).
tff(203,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
( ( nil = app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) )
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) ),
inference(unit_resolution,[status(thm)],[204,198,188,71]) ).
tff(206,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil,
inference(unit_resolution,[status(thm)],[205,185]) ).
tff(207,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[206,182]) ).
tff(208,plain,
( ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,plain,
( ( ( cons(sk9,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,axiom,
( ( cons(sk9,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(211,plain,
( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[211,208]) ).
tff(213,plain,
cons(sk9,nil) = sk3,
inference(unit_resolution,[status(thm)],[212,207]) ).
tff(214,plain,
cons(sk9,nil) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(transitivity,[status(thm)],[213,177,173]) ).
tff(215,plain,
( frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))))
<=> frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(monotonicity,[status(thm)],[214,169]) ).
tff(216,plain,
( frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
<=> frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) ),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
( ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(218,plain,
( ssList(sk3)
<=> ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(221,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)),
inference(modus_ponens,[status(thm)],[221,218]) ).
tff(223,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) )),
inference(bind,[status(th)],[]) ).
tff(224,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(quant_intro,[status(thm)],[223]) ).
tff(225,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,plain,
^ [V: $i,U: $i] :
rewrite(( ( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) )),
inference(bind,[status(th)],[]) ).
tff(227,plain,
( ! [V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(quant_intro,[status(thm)],[226]) ).
tff(228,plain,
( ! [W: $i,V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) )
<=> ! [V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(229,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) )
<=> ! [W: $i,V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(230,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) )
<=> ! [V: $i,U: $i] :
( frontsegP(app(U,V),U)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V)) ) ),
inference(transitivity,[status(thm)],[229,228]) ).
tff(231,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(transitivity,[status(thm)],[230,227]) ).
tff(232,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != W )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(W) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) ) )),
( ( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) ) )),
inference(bind,[status(th)],[]) ).
tff(233,plain,
( ! [W: $i,V: $i,U: $i] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| frontsegP(W,U) ) ),
inference(quant_intro,[status(thm)],[232]) ).
tff(234,plain,
( ! [W: $i,V: $i,U: $i] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ) ),
inference(transitivity,[status(thm)],[233,231]) ).
tff(235,axiom,
! [W: $i,V: $i,U: $i] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause144) ).
tff(236,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ),
inference(modus_ponens,[status(thm)],[235,234]) ).
tff(237,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ),
inference(modus_ponens,[status(thm)],[236,225]) ).
tff(238,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ),
inference(skolemize,[status(sab)],[237]) ).
tff(239,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) ),
inference(modus_ponens,[status(thm)],[238,224]) ).
tff(240,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(241,plain,
( ( ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(sk8)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
<=> ( ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(242,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(sk8)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ) ),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(sk8)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ) ),
inference(transitivity,[status(thm)],[242,240]) ).
tff(244,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(sk8)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| frontsegP(app(U,V),U) )
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(modus_ponens,[status(thm)],[244,243]) ).
tff(246,plain,
( ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(unit_resolution,[status(thm)],[245,239,188,71]) ).
tff(247,plain,
frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),app(app(sk7,cons(sk5,nil)),cons(sk6,nil))),
inference(unit_resolution,[status(thm)],[246,222]) ).
tff(248,plain,
frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))),
inference(modus_ponens,[status(thm)],[247,216]) ).
tff(249,plain,
( ( tl(app(cons(sk6,nil),nil)) = tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))) )
<=> ( tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))) = tl(app(cons(sk6,nil),nil)) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(250,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(251,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[250]) ).
tff(252,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(253,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(254,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[253]) ).
tff(255,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(256,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[256,252]) ).
tff(258,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[257]) ).
tff(259,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[258,251]) ).
tff(260,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(cons(sk6,nil),nil) = cons(sk6,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(cons(sk6,nil),nil) = cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(261,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(cons(sk6,nil),nil) = cons(sk6,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(262,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(cons(sk6,nil),nil) = cons(sk6,nil) ) ),
inference(modus_ponens,[status(thm)],[261,260]) ).
tff(263,plain,
app(cons(sk6,nil),nil) = cons(sk6,nil),
inference(unit_resolution,[status(thm)],[262,16,259,3]) ).
tff(264,plain,
tl(app(cons(sk6,nil),nil)) = tl(cons(sk6,nil)),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
tl(cons(sk6,nil)) = tl(app(cons(sk6,nil),nil)),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(267,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(quant_intro,[status(thm)],[266]) ).
tff(268,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(269,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(270,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(quant_intro,[status(thm)],[269]) ).
tff(271,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
tff(272,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[271,270]) ).
tff(273,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[272,268]) ).
tff(274,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(skolemize,[status(sab)],[273]) ).
tff(275,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[274,267]) ).
tff(276,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( tl(cons(sk6,nil)) = nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( tl(cons(sk6,nil)) = nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(277,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( tl(cons(sk6,nil)) = nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(278,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( tl(cons(sk6,nil)) = nil ) ),
inference(modus_ponens,[status(thm)],[277,276]) ).
tff(279,plain,
tl(cons(sk6,nil)) = nil,
inference(unit_resolution,[status(thm)],[278,16,275,3]) ).
tff(280,plain,
nil = tl(cons(sk6,nil)),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
nil = tl(app(cons(sk6,nil),nil)),
inference(transitivity,[status(thm)],[280,265]) ).
tff(282,plain,
( ( nil = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
<=> ( tl(app(cons(sk6,nil),nil)) = tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))) ) ),
inference(monotonicity,[status(thm)],[281,131]) ).
tff(283,plain,
( ( nil = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
<=> ( tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))) = tl(app(cons(sk6,nil),nil)) ) ),
inference(transitivity,[status(thm)],[282,249]) ).
tff(284,plain,
( ( tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))) = tl(app(cons(sk6,nil),nil)) )
<=> ( nil = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ) ),
inference(symmetry,[status(thm)],[283]) ).
tff(285,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
inference(bind,[status(th)],[]) ).
tff(286,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) ),
inference(quant_intro,[status(thm)],[285]) ).
tff(287,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(288,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) )),
inference(bind,[status(th)],[]) ).
tff(289,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ) ),
inference(quant_intro,[status(thm)],[288]) ).
tff(290,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause133) ).
tff(291,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[291,287]) ).
tff(293,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(skolemize,[status(sab)],[292]) ).
tff(294,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[293,286]) ).
tff(295,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,nil)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,nil)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(296,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,nil)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(297,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,nil)) ) ),
inference(modus_ponens,[status(thm)],[296,295]) ).
tff(298,plain,
( ( nil = app(sk7,cons(sk5,nil)) )
| ( tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,nil)) ) ),
inference(unit_resolution,[status(thm)],[297,294,20,67]) ).
tff(299,plain,
tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[298,150]) ).
tff(300,plain,
app(tl(app(sk7,cons(sk5,nil))),cons(sk6,nil)) = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))),
inference(symmetry,[status(thm)],[299]) ).
tff(301,plain,
app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,nil)),
inference(monotonicity,[status(thm)],[263]) ).
tff(302,plain,
app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) = tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))),
inference(transitivity,[status(thm)],[301,300,131]) ).
tff(303,plain,
( ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) = nil )
<=> ( tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))) = tl(app(cons(sk6,nil),nil)) ) ),
inference(monotonicity,[status(thm)],[302,281]) ).
tff(304,plain,
( ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) = nil )
<=> ( nil = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ) ),
inference(transitivity,[status(thm)],[303,284]) ).
tff(305,plain,
( ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil )
<=> ( nil != tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ) ),
inference(monotonicity,[status(thm)],[304]) ).
tff(306,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(307,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[306]) ).
tff(308,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(309,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(310,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[309]) ).
tff(311,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(312,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[311,310]) ).
tff(313,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[312,308]) ).
tff(314,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(skolemize,[status(sab)],[313]) ).
tff(315,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[314,307]) ).
tff(316,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ssList(tl(app(sk7,cons(sk5,nil)))) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ssList(tl(app(sk7,cons(sk5,nil)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(317,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ssList(tl(app(sk7,cons(sk5,nil)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ssList(tl(app(sk7,cons(sk5,nil)))) ),
inference(modus_ponens,[status(thm)],[317,316]) ).
tff(319,plain,
ssList(tl(app(sk7,cons(sk5,nil)))),
inference(unit_resolution,[status(thm)],[318,315,67,150]) ).
tff(320,plain,
( ( nil = app(cons(sk6,nil),nil) )
<=> ( nil = cons(sk6,nil) ) ),
inference(monotonicity,[status(thm)],[263]) ).
tff(321,plain,
( ( nil = app(cons(sk6,nil),nil) )
<=> ( cons(sk6,nil) = nil ) ),
inference(transitivity,[status(thm)],[320,78]) ).
tff(322,plain,
( ( cons(sk6,nil) = nil )
<=> ( nil = app(cons(sk6,nil),nil) ) ),
inference(symmetry,[status(thm)],[321]) ).
tff(323,plain,
( ( cons(sk6,nil) != nil )
<=> ( nil != app(cons(sk6,nil),nil) ) ),
inference(monotonicity,[status(thm)],[322]) ).
tff(324,plain,
nil != app(cons(sk6,nil),nil),
inference(modus_ponens,[status(thm)],[94,323]) ).
tff(325,plain,
( ssList(app(cons(sk6,nil),nil))
<=> ssList(cons(sk6,nil)) ),
inference(monotonicity,[status(thm)],[263]) ).
tff(326,plain,
( ssList(cons(sk6,nil))
<=> ssList(app(cons(sk6,nil),nil)) ),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
ssList(app(cons(sk6,nil),nil)),
inference(modus_ponens,[status(thm)],[20,326]) ).
tff(328,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(329,plain,
( ( ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ~ ssList(app(cons(sk6,nil),nil))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil )
| ( nil = app(cons(sk6,nil),nil) ) )
<=> ( ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(330,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ~ ssList(app(cons(sk6,nil),nil))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil )
| ( nil = app(cons(sk6,nil),nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil ) ) ),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ~ ssList(app(cons(sk6,nil),nil))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil )
| ( nil = app(cons(sk6,nil),nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil ) ) ),
inference(transitivity,[status(thm)],[330,328]) ).
tff(332,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ~ ssList(app(cons(sk6,nil),nil))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil )
| ( nil = app(cons(sk6,nil),nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil ) ),
inference(modus_ponens,[status(thm)],[332,331]) ).
tff(334,plain,
( ~ ssList(tl(app(sk7,cons(sk5,nil))))
| ( app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil ) ),
inference(unit_resolution,[status(thm)],[333,105,327,324]) ).
tff(335,plain,
app(tl(app(sk7,cons(sk5,nil))),app(cons(sk6,nil),nil)) != nil,
inference(unit_resolution,[status(thm)],[334,319]) ).
tff(336,plain,
nil != tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))),
inference(modus_ponens,[status(thm)],[335,305]) ).
tff(337,plain,
( ssList(tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil)))))
<=> ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(338,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
| ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
| ssList(tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
| ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
| ssList(tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(339,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
| ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
| ssList(tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(340,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))
| ( nil = app(sk7,app(cons(sk5,nil),cons(sk6,nil))) )
| ssList(tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))) ),
inference(modus_ponens,[status(thm)],[339,338]) ).
tff(341,plain,
ssList(tl(app(sk7,app(cons(sk5,nil),cons(sk6,nil))))),
inference(unit_resolution,[status(thm)],[340,315,72,114]) ).
tff(342,plain,
ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))),
inference(modus_ponens,[status(thm)],[341,337]) ).
tff(343,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(344,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[343]) ).
tff(345,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(346,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ frontsegP(nil,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ frontsegP(nil,U) ) )),
( ( ~ frontsegP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ frontsegP(nil,U)
| ( nil = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ frontsegP(nil,U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) )),
( ( ~ frontsegP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(347,plain,
( ! [U: $i] :
( ~ frontsegP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[346]) ).
tff(348,axiom,
! [U: $i] :
( ~ frontsegP(nil,U)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause84) ).
tff(349,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[348,347]) ).
tff(350,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[349,345]) ).
tff(351,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ),
inference(skolemize,[status(sab)],[350]) ).
tff(352,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[351,344]) ).
tff(353,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ( nil = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
| ~ frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ( nil = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
| ~ frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(354,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ( nil = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
| ~ frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(355,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ( nil = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) )
| ~ frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))) ),
inference(modus_ponens,[status(thm)],[354,353]) ).
tff(356,plain,
~ frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))),
inference(unit_resolution,[status(thm)],[355,352,342,336]) ).
tff(357,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(358,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[357]) ).
tff(359,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(360,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(361,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[360]) ).
tff(362,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(363,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[362,361]) ).
tff(364,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[363,359]) ).
tff(365,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[364]) ).
tff(366,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[365,358]) ).
tff(367,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ssItem(hd(app(sk7,cons(sk5,nil)))) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ssItem(hd(app(sk7,cons(sk5,nil)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(368,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ssItem(hd(app(sk7,cons(sk5,nil)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(369,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ssItem(hd(app(sk7,cons(sk5,nil)))) ),
inference(modus_ponens,[status(thm)],[368,367]) ).
tff(370,plain,
( ( nil = app(sk7,cons(sk5,nil)) )
| ssItem(hd(app(sk7,cons(sk5,nil)))) ),
inference(unit_resolution,[status(thm)],[369,366,67]) ).
tff(371,plain,
ssItem(hd(app(sk7,cons(sk5,nil)))),
inference(unit_resolution,[status(thm)],[370,150]) ).
tff(372,plain,
( ( ssItem(sk9)
| ( nil = sk3 ) )
<=> ( ssItem(sk9)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(373,axiom,
( ssItem(sk9)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(374,plain,
( ssItem(sk9)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[373,372]) ).
tff(375,plain,
ssItem(sk9),
inference(unit_resolution,[status(thm)],[374,207]) ).
tff(376,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(377,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) ),
inference(quant_intro,[status(thm)],[376]) ).
tff(378,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(379,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
( ( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
( ( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
( ( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssItem(W) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(V)
| ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
( ( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
( ( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssItem(U) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
( ( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
( ( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ ssItem(U)
| frontsegP(V,X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X))
| frontsegP(V,X) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X))
| frontsegP(V,X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
( ( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ ssItem(U)
| frontsegP(V,X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(380,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ ssItem(U)
| frontsegP(V,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ) ),
inference(quant_intro,[status(thm)],[379]) ).
tff(381,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ ssItem(U)
| frontsegP(V,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause174) ).
tff(382,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ),
inference(modus_ponens,[status(thm)],[381,380]) ).
tff(383,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ),
inference(modus_ponens,[status(thm)],[382,378]) ).
tff(384,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ),
inference(skolemize,[status(sab)],[383]) ).
tff(385,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) ),
inference(modus_ponens,[status(thm)],[384,377]) ).
tff(386,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
| ~ ssList(nil)
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
| ~ ssList(nil)
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(387,plain,
( ( ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ ssList(nil)
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(388,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ ssList(nil)
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
| ~ ssList(nil)
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) ) ),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ ssList(nil)
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
| ~ ssList(nil)
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) ) ),
inference(transitivity,[status(thm)],[388,386]) ).
tff(390,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ ssList(nil)
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(391,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| frontsegP(V,X)
| ~ ssItem(W)
| ~ frontsegP(cons(U,V),cons(W,X)) )
| ~ ssList(nil)
| ~ ssItem(hd(app(sk7,cons(sk5,nil))))
| ~ ssList(tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ ssItem(sk9)
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) ),
inference(modus_ponens,[status(thm)],[390,389]) ).
tff(392,plain,
( frontsegP(nil,tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))
| ~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))) ),
inference(unit_resolution,[status(thm)],[391,16,385,375,371,342]) ).
tff(393,plain,
~ frontsegP(cons(sk9,nil),cons(hd(app(sk7,cons(sk5,nil))),tl(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))))),
inference(unit_resolution,[status(thm)],[392,356]) ).
tff(394,plain,
$false,
inference(unit_resolution,[status(thm)],[393,248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC164-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 08:29:18 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.98/5.16 % SZS status Unsatisfiable
% 4.98/5.16 % SZS output start Proof
% See solution above
% 4.98/5.22 % E exiting
%------------------------------------------------------------------------------