TSTP Solution File: SWC188-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC188-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 : Tue Sep 20 11:55:59 EDT 2022
% Result : Unsatisfiable 16.09s 10.27s
% Output : Proof 16.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 163
% Syntax : Number of formulae : 369 ( 100 unt; 19 typ; 0 def)
% Number of atoms : 2395 ( 597 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 3650 (1746 ~;1700 |; 0 &)
% ( 204 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 141 ( 141 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 11 >; 5 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 664 ( 599 !; 0 ?; 664 :)
% Comments :
%------------------------------------------------------------------------------
tff(nil_type,type,
nil: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(skaf82_type,type,
skaf82: $i > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(sk9_type,type,
sk9: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(singletonP_type,type,
singletonP: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(skaf83_type,type,
skaf83: $i > $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(1,plain,
( ( nil = cons(sk6,nil) )
<=> ( cons(sk6,nil) = nil ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( cons(sk6,nil) = nil )
<=> ( nil = cons(sk6,nil) ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(3,plain,
( ( cons(sk6,nil) != nil )
<=> ( nil != cons(sk6,nil) ) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(6,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( cons(U,nil) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,nil) != V )
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssItem(U)
| ( cons(U,nil) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V )
| singletonP(V) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V )
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V: $i,U: $i] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V: $i,U: $i] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
tff(13,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ~ singletonP(nil)
<=> ~ singletonP(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause11) ).
tff(19,plain,
~ singletonP(nil),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(22,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ ssItem(sk6)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk6,nil) != nil ) )
<=> ( singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk6,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk6,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk6,nil) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
cons(sk6,nil) != nil,
inference(unit_resolution,[status(thm)],[28,22,19,16,6]) ).
tff(30,plain,
nil != cons(sk6,nil),
inference(modus_ponens,[status(thm)],[29,3]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34]) ).
tff(36,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,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(42,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(43,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)],[42,41]) ).
tff(44,plain,
ssList(cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[43,22,40,6]) ).
tff(45,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
^ [U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ segmentP(nil,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause80) ).
tff(51,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(cons(sk6,nil))
| ( nil = cons(sk6,nil) )
| ~ segmentP(nil,cons(sk6,nil)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(cons(sk6,nil))
| ( nil = cons(sk6,nil) )
| ~ segmentP(nil,cons(sk6,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(cons(sk6,nil))
| ( nil = cons(sk6,nil) )
| ~ segmentP(nil,cons(sk6,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(cons(sk6,nil))
| ( nil = cons(sk6,nil) )
| ~ segmentP(nil,cons(sk6,nil)) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
~ segmentP(nil,cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[57,54,44,30]) ).
tff(59,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(61,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,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(63,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(64,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)],[63,62]) ).
tff(65,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[64,22,40,61]) ).
tff(66,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(68,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,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(70,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)],[69]) ).
tff(71,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(72,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(73,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)],[72]) ).
tff(74,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(75,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk7) )
<=> ( ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,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(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,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(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,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(84,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
ssList(app(sk7,cons(sk5,nil))),
inference(unit_resolution,[status(thm)],[84,78,68,65]) ).
tff(86,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(88,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(app(U,V),W) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| segmentP(X,V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).
tff(95,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| segmentP(nil,cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| segmentP(nil,cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| segmentP(nil,cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| segmentP(nil,cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil,
inference(unit_resolution,[status(thm)],[104,22,98,88,44,85,58]) ).
tff(106,plain,
( ssList(sk3)
<=> ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(110,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[110,107]) ).
tff(112,plain,
ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)),
inference(modus_ponens,[status(thm)],[111,106]) ).
tff(113,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| frontsegP(U,nil) )
<=> ( ~ ssList(U)
| frontsegP(U,nil) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,axiom,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
tff(117,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,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),nil) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,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),nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,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),nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,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),nil) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil),
inference(unit_resolution,[status(thm)],[122,119,112]) ).
tff(124,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ( V = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,axiom,
! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause129) ).
tff(130,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(modus_ponens,[status(thm)],[132,125]) ).
tff(134,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil)
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) )
<=> ( ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil)
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil)
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil)
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil ) ),
inference(unit_resolution,[status(thm)],[139,22,133,112,123]) ).
tff(141,plain,
~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)),
inference(unit_resolution,[status(thm)],[140,105]) ).
tff(142,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(143,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
^ [U: $i] :
trans(
monotonicity(
rewrite(
( ( ( nil != U )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U ) ) )),
( ( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
rewrite(
( ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
( ( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(146,plain,
( ! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,axiom,
! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause83) ).
tff(148,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[150,143]) ).
tff(152,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
( ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(unit_resolution,[status(thm)],[154,151,112]) ).
tff(156,plain,
nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(unit_resolution,[status(thm)],[155,141]) ).
tff(157,plain,
( ( ssItem(sk9)
| ( nil = sk3 ) )
<=> ( ssItem(sk9)
| ( nil = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ( ssItem(sk9)
| ( nil = sk3 ) )
<=> ( ssItem(sk9)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,axiom,
( ssItem(sk9)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(160,plain,
( ssItem(sk9)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
( ssItem(sk9)
| ( nil = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ),
inference(modus_ponens,[status(thm)],[160,157]) ).
tff(162,plain,
ssItem(sk9),
inference(unit_resolution,[status(thm)],[161,156]) ).
tff(163,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(164,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)],[163]) ).
tff(165,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(166,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(167,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)],[166]) ).
tff(168,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(169,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[171,164]) ).
tff(173,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk9)
| ~ ssList(nil)
| ( tl(cons(sk9,nil)) = nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk9)
| ~ ssList(nil)
| ( tl(cons(sk9,nil)) = nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(174,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk9)
| ~ ssList(nil)
| ( tl(cons(sk9,nil)) = nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk9)
| ~ ssList(nil)
| ( tl(cons(sk9,nil)) = nil ) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
tl(cons(sk9,nil)) = nil,
inference(unit_resolution,[status(thm)],[175,22,172,162]) ).
tff(177,plain,
( ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) )
<=> ( ( nil = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| ( cons(sk9,nil) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ( ( cons(sk9,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,axiom,
( ( cons(sk9,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(181,plain,
( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[181,178]) ).
tff(183,plain,
( ( nil = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| ( cons(sk9,nil) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ),
inference(modus_ponens,[status(thm)],[182,177]) ).
tff(184,plain,
cons(sk9,nil) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(unit_resolution,[status(thm)],[183,156]) ).
tff(185,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = cons(sk9,nil),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
tl(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) = tl(cons(sk9,nil)),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,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(188,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)],[187]) ).
tff(189,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(190,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(191,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)],[190]) ).
tff(192,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(193,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)],[192,191]) ).
tff(194,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)],[193,189]) ).
tff(195,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)],[194]) ).
tff(196,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)],[195,188]) ).
tff(197,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(198,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(199,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) ) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)),
inference(unit_resolution,[status(thm)],[199,196,88,44,85]) ).
tff(201,plain,
app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(symmetry,[status(thm)],[200]) ).
tff(202,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(203,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)],[202]) ).
tff(204,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(205,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(206,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)],[205]) ).
tff(207,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(208,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[208,204]) ).
tff(210,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[209]) ).
tff(211,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[210,203]) ).
tff(212,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( app(cons(sk6,nil),sk8) = cons(sk6,sk8) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( app(cons(sk6,nil),sk8) = cons(sk6,sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( app(cons(sk6,nil),sk8) = cons(sk6,sk8) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( app(cons(sk6,nil),sk8) = cons(sk6,sk8) ) ),
inference(modus_ponens,[status(thm)],[213,212]) ).
tff(215,plain,
app(cons(sk6,nil),sk8) = cons(sk6,sk8),
inference(unit_resolution,[status(thm)],[214,211,6,88]) ).
tff(216,plain,
cons(sk6,sk8) = app(cons(sk6,nil),sk8),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
app(app(sk7,cons(sk5,nil)),cons(sk6,sk8)) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)),
inference(monotonicity,[status(thm)],[216]) ).
tff(218,plain,
app(app(sk7,cons(sk5,nil)),cons(sk6,sk8)) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(transitivity,[status(thm)],[217,201]) ).
tff(219,plain,
tl(app(app(sk7,cons(sk5,nil)),cons(sk6,sk8))) = tl(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
( ssList(cons(sk6,sk8))
<=> ssList(app(cons(sk6,nil),sk8)) ),
inference(monotonicity,[status(thm)],[216]) ).
tff(221,plain,
( ssList(app(cons(sk6,nil),sk8))
<=> ssList(cons(sk6,sk8)) ),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(223,plain,
( ( ~ ssList(sk8)
| ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil)) )
<=> ( ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(224,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ) ),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ) ),
inference(transitivity,[status(thm)],[224,222]) ).
tff(226,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
ssList(app(cons(sk6,nil),sk8)),
inference(unit_resolution,[status(thm)],[227,78,88,44]) ).
tff(229,plain,
ssList(cons(sk6,sk8)),
inference(modus_ponens,[status(thm)],[228,221]) ).
tff(230,plain,
( ( nil = app(sk7,cons(sk5,nil)) )
<=> ( app(sk7,cons(sk5,nil)) = nil ) ),
inference(commutativity,[status(thm)],]) ).
tff(231,plain,
( ( app(sk7,cons(sk5,nil)) = nil )
<=> ( nil = app(sk7,cons(sk5,nil)) ) ),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
( ( app(sk7,cons(sk5,nil)) != nil )
<=> ( nil != app(sk7,cons(sk5,nil)) ) ),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
( ( nil = cons(sk5,nil) )
<=> ( cons(sk5,nil) = nil ) ),
inference(commutativity,[status(thm)],]) ).
tff(234,plain,
( ( cons(sk5,nil) = nil )
<=> ( nil = cons(sk5,nil) ) ),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
( ( cons(sk5,nil) != nil )
<=> ( nil != cons(sk5,nil) ) ),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,plain,
( ( ~ ssItem(sk5)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk5,nil) != nil ) )
<=> ( singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(238,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk5,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != nil ) ) ),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk5,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != nil ) ) ),
inference(transitivity,[status(thm)],[238,236]) ).
tff(240,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk5,nil) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(241,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
cons(sk5,nil) != nil,
inference(unit_resolution,[status(thm)],[241,22,19,16,61]) ).
tff(243,plain,
nil != cons(sk5,nil),
inference(modus_ponens,[status(thm)],[242,235]) ).
tff(244,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(245,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)],[244]) ).
tff(246,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(247,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(248,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)],[247]) ).
tff(249,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(250,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[249,248]) ).
tff(251,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[250,246]) ).
tff(252,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(skolemize,[status(sab)],[251]) ).
tff(253,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[252,245]) ).
tff(254,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(255,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(256,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)],[255,254]) ).
tff(257,plain,
( ( app(sk7,cons(sk5,nil)) != nil )
| ( nil = cons(sk5,nil) ) ),
inference(unit_resolution,[status(thm)],[256,253,68,65]) ).
tff(258,plain,
app(sk7,cons(sk5,nil)) != nil,
inference(unit_resolution,[status(thm)],[257,243]) ).
tff(259,plain,
nil != app(sk7,cons(sk5,nil)),
inference(modus_ponens,[status(thm)],[258,232]) ).
tff(260,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(261,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)],[260]) ).
tff(262,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(263,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(264,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)],[263]) ).
tff(265,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(266,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[266,262]) ).
tff(268,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(skolemize,[status(sab)],[267]) ).
tff(269,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
inference(modus_ponens,[status(thm)],[268,261]) ).
tff(270,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(sk6,sk8))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( tl(app(app(sk7,cons(sk5,nil)),cons(sk6,sk8))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(sk6,sk8))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( tl(app(app(sk7,cons(sk5,nil)),cons(sk6,sk8))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(271,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(sk6,sk8))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( tl(app(app(sk7,cons(sk5,nil)),cons(sk6,sk8))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(272,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) )
| ~ ssList(cons(sk6,sk8))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( tl(app(app(sk7,cons(sk5,nil)),cons(sk6,sk8))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) ) ),
inference(modus_ponens,[status(thm)],[271,270]) ).
tff(273,plain,
tl(app(app(sk7,cons(sk5,nil)),cons(sk6,sk8))) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,sk8)),
inference(unit_resolution,[status(thm)],[272,269,85,259,229]) ).
tff(274,plain,
app(tl(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) = tl(app(app(sk7,cons(sk5,nil)),cons(sk6,sk8))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(276,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[275]) ).
tff(277,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(278,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(279,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[278]) ).
tff(280,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(281,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[280,279]) ).
tff(282,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[281,277]) ).
tff(283,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[282]) ).
tff(284,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[283,276]) ).
tff(285,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil)))) = app(sk7,cons(sk5,nil)) ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil)))) = app(sk7,cons(sk5,nil)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(286,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil)))) = app(sk7,cons(sk5,nil)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(287,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( nil = app(sk7,cons(sk5,nil)) )
| ( cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil)))) = app(sk7,cons(sk5,nil)) ) ),
inference(modus_ponens,[status(thm)],[286,285]) ).
tff(288,plain,
( ( nil = app(sk7,cons(sk5,nil)) )
| ( cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil)))) = app(sk7,cons(sk5,nil)) ) ),
inference(unit_resolution,[status(thm)],[287,284,85]) ).
tff(289,plain,
cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil)))) = app(sk7,cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[288,259]) ).
tff(290,plain,
app(sk7,cons(sk5,nil)) = cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil)))),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
tl(app(sk7,cons(sk5,nil))) = tl(cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil))))),
inference(monotonicity,[status(thm)],[290]) ).
tff(292,plain,
tl(cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil))))) = tl(app(sk7,cons(sk5,nil))),
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
^ [U: $i] :
refl(
( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],]) ).
tff(294,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[293]) ).
tff(295,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(296,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(297,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[296,295]) ).
tff(298,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[297]) ).
tff(299,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[298,294]) ).
tff(300,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(app(sk7,cons(sk5,nil)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(301,plain,
ssList(skaf82(app(sk7,cons(sk5,nil)))),
inference(unit_resolution,[status(thm)],[300,299]) ).
tff(302,plain,
^ [U: $i] :
refl(
( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],]) ).
tff(303,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[302]) ).
tff(304,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],]) ).
tff(305,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(306,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[305,304]) ).
tff(307,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[306]) ).
tff(308,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[307,303]) ).
tff(309,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(app(sk7,cons(sk5,nil)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(310,plain,
ssItem(skaf83(app(sk7,cons(sk5,nil)))),
inference(unit_resolution,[status(thm)],[309,308]) ).
tff(311,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf83(app(sk7,cons(sk5,nil))))
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( tl(cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil))))) = skaf82(app(sk7,cons(sk5,nil))) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf83(app(sk7,cons(sk5,nil))))
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( tl(cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil))))) = skaf82(app(sk7,cons(sk5,nil))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(312,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf83(app(sk7,cons(sk5,nil))))
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( tl(cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil))))) = skaf82(app(sk7,cons(sk5,nil))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(313,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(skaf83(app(sk7,cons(sk5,nil))))
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( tl(cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil))))) = skaf82(app(sk7,cons(sk5,nil))) ) ),
inference(modus_ponens,[status(thm)],[312,311]) ).
tff(314,plain,
( ~ ssItem(skaf83(app(sk7,cons(sk5,nil))))
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( tl(cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil))))) = skaf82(app(sk7,cons(sk5,nil))) ) ),
inference(unit_resolution,[status(thm)],[313,172]) ).
tff(315,plain,
tl(cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil))))) = skaf82(app(sk7,cons(sk5,nil))),
inference(unit_resolution,[status(thm)],[314,310,301]) ).
tff(316,plain,
skaf82(app(sk7,cons(sk5,nil))) = tl(cons(skaf83(app(sk7,cons(sk5,nil))),skaf82(app(sk7,cons(sk5,nil))))),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
skaf82(app(sk7,cons(sk5,nil))) = tl(app(sk7,cons(sk5,nil))),
inference(transitivity,[status(thm)],[316,292]) ).
tff(318,plain,
app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) = app(tl(app(sk7,cons(sk5,nil))),cons(sk6,sk8)),
inference(monotonicity,[status(thm)],[317]) ).
tff(319,plain,
app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) = nil,
inference(transitivity,[status(thm)],[318,274,219,186,176]) ).
tff(320,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(321,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[320]) ).
tff(322,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(323,plain,
^ [U: $i] :
rewrite(
( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(324,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[323]) ).
tff(325,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(326,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[325,324]) ).
tff(327,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[326,322]) ).
tff(328,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[327]) ).
tff(329,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[328,321]) ).
tff(330,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk6)
| ~ memberP(nil,sk6) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk6)
| ~ memberP(nil,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(331,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk6)
| ~ memberP(nil,sk6) ),
inference(quant_inst,[status(thm)],]) ).
tff(332,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk6)
| ~ memberP(nil,sk6) ),
inference(modus_ponens,[status(thm)],[331,330]) ).
tff(333,plain,
~ memberP(nil,sk6),
inference(unit_resolution,[status(thm)],[332,329,6]) ).
tff(334,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(335,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[334]) ).
tff(336,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(337,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(338,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[337]) ).
tff(339,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause175) ).
tff(340,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[339,338]) ).
tff(341,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[340,336]) ).
tff(342,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(skolemize,[status(sab)],[341]) ).
tff(343,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[342,335]) ).
tff(344,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(345,plain,
( ( ~ ssList(nil)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(sk8)
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(346,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(sk8)
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) ) ),
inference(monotonicity,[status(thm)],[345]) ).
tff(347,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(sk8)
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) ) ),
inference(transitivity,[status(thm)],[346,344]) ).
tff(348,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(sk8)
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(349,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| memberP(nil,sk6)
| ~ ssList(skaf82(app(sk7,cons(sk5,nil))))
| ( app(skaf82(app(sk7,cons(sk5,nil))),cons(sk6,sk8)) != nil ) ),
inference(modus_ponens,[status(thm)],[348,347]) ).
tff(350,plain,
$false,
inference(unit_resolution,[status(thm)],[349,22,343,6,88,333,301,319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWC188-1 : TPTP v8.1.0. Released v2.4.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat Sep 3 22:44:18 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 16.09/10.27 % SZS status Unsatisfiable
% 16.09/10.27 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------