%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC166-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:30:23 AM UTC 2025
% Result : Unsatisfiable 0.99s 1.17s
% Output : Proof 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 84
% Syntax : Number of formulae : 195 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 1500 ( 180 equ)
% Maximal formula atoms : 34 ( 7 avg)
% Number of connectives : 2412 (1179 ~;1121 |; 0 &)
% ( 112 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 72 ( 72 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 444 ( 401 !; 0 ?; 444 :)
% Comments :
%------------------------------------------------------------------------------
tff(cyclefreeP_type,type,
cyclefreeP: $i > $o ).
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(nil_type,type,
nil: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(skaf44_type,type,
skaf44: $i > $i ).
tff(singletonP_type,type,
singletonP: $i > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,axiom,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(6,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(9,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,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)],[13]) ).
tff(15,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(16,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
ssList(nil),
file('/export/starexec/sandbox2/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)
| 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(24,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(25,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)],[24,23]) ).
tff(26,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[25,22,19,9]) ).
tff(27,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(29,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,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(31,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)],[30]) ).
tff(32,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(33,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(34,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)],[33]) ).
tff(35,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(36,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,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(41,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(42,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)],[41]) ).
tff(43,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)],[42,40]) ).
tff(44,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(45,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)],[44,43]) ).
tff(46,plain,
ssList(app(sk7,cons(sk5,nil))),
inference(unit_resolution,[status(thm)],[45,39,29,26]) ).
tff(47,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(49,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,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(51,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(52,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)],[51,50]) ).
tff(53,plain,
ssList(cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[52,22,19,49]) ).
tff(54,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(56,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,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)],[60]) ).
tff(62,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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(63,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)],[62,61]) ).
tff(64,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)],[63,59]) ).
tff(65,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)],[64]) ).
tff(66,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)],[65,58]) ).
tff(67,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(68,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(69,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)],[68,67]) ).
tff(70,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)],[69,66,56,53,46]) ).
tff(71,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)],[70]) ).
tff(72,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(73,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)],[72]) ).
tff(74,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(75,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(76,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)],[75]) ).
tff(77,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(78,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,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(83,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(84,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)],[83,82]) ).
tff(85,plain,
app(cons(sk6,nil),sk8) = cons(sk6,sk8),
inference(unit_resolution,[status(thm)],[84,81,49,56]) ).
tff(86,plain,
cons(sk6,sk8) = app(cons(sk6,nil),sk8),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
( ~ neq(sk5,sk6)
<=> ~ neq(sk5,sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
~ neq(sk5,sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(89,plain,
~ neq(sk5,sk6),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U) )
<=> ( ~ ssItem(U)
| neq(V,U)
| ~ ssItem(V) ) )),
( ( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssItem(U)
| neq(V,U)
| ~ ssItem(V)
| ( V = U ) ) )),
rewrite(( ( ~ ssItem(U)
| neq(V,U)
| ~ ssItem(V)
| ( V = U ) )
<=> ( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) )),
( ( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause102) ).
tff(96,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ssItem(sk6)
| ( sk5 = sk6 )
| neq(sk5,sk6)
| ~ ssItem(sk5) )
<=> ( neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| ~ ssItem(sk6)
| ( sk5 = sk6 )
| neq(sk5,sk6)
| ~ ssItem(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| ~ ssItem(sk6)
| ( sk5 = sk6 )
| neq(sk5,sk6)
| ~ ssItem(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ) ),
inference(transitivity,[status(thm)],[102,100]) ).
tff(104,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| ~ ssItem(sk6)
| ( sk5 = sk6 )
| neq(sk5,sk6)
| ~ ssItem(sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
sk5 = sk6,
inference(unit_resolution,[status(thm)],[105,99,9,49,89]) ).
tff(107,plain,
cons(sk5,nil) = cons(sk6,nil),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
cons(sk6,nil) = cons(sk5,nil),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
app(sk7,cons(sk6,nil)) = app(sk7,cons(sk5,nil)),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)),
inference(monotonicity,[status(thm)],[109,86]) ).
tff(111,plain,
app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) = sk3,
inference(transitivity,[status(thm)],[110,71,6,3]) ).
tff(112,plain,
( cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
<=> cyclefreeP(sk3) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( cyclefreeP(sk3)
<=> cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))) ),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( singletonP(sk3)
<=> singletonP(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,axiom,
singletonP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(116,plain,
singletonP(sk3),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(119,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
<=> ( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,plain,
^ [U: $i] :
rewrite(( ( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) )
<=> ( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) )),
inference(bind,[status(th)],[]) ).
tff(124,plain,
( ! [U: $i] :
( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,axiom,
! [U: $i] :
( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
tff(126,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(skolemize,[status(sab)],[127]) ).
tff(129,plain,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) ),
inference(modus_ponens,[status(thm)],[128,121]) ).
tff(130,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
| ~ ssList(sk3)
| ( cons(skaf44(sk3),nil) = sk3 )
| ~ singletonP(sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
| ~ ssList(sk3)
| ( cons(skaf44(sk3),nil) = sk3 )
| ~ singletonP(sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
| ~ ssList(sk3)
| ( cons(skaf44(sk3),nil) = sk3 )
| ~ singletonP(sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf44(U),nil) = U )
| ~ singletonP(U) )
| ~ ssList(sk3)
| ( cons(skaf44(sk3),nil) = sk3 )
| ~ singletonP(sk3) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
cons(skaf44(sk3),nil) = sk3,
inference(unit_resolution,[status(thm)],[132,129,119,116]) ).
tff(134,plain,
( cyclefreeP(cons(skaf44(sk3),nil))
<=> cyclefreeP(sk3) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
^ [U: $i] :
refl(( ssItem(skaf44(U))
<=> ssItem(skaf44(U)) )),
inference(bind,[status(th)],[]) ).
tff(136,plain,
( ! [U: $i] : ssItem(skaf44(U))
<=> ! [U: $i] : ssItem(skaf44(U)) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [U: $i] : ssItem(skaf44(U))
<=> ! [U: $i] : ssItem(skaf44(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,axiom,
! [U: $i] : ssItem(skaf44(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause47) ).
tff(139,plain,
! [U: $i] : ssItem(skaf44(U)),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [U: $i] : ssItem(skaf44(U)),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [U: $i] : ssItem(skaf44(U)),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
( ~ ! [U: $i] : ssItem(skaf44(U))
| ssItem(skaf44(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
ssItem(skaf44(sk3)),
inference(unit_resolution,[status(thm)],[142,141]) ).
tff(144,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) )
<=> ( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) )
<=> ! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) )
<=> ! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,axiom,
! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause70) ).
tff(148,plain,
! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) )
| ~ ssItem(skaf44(sk3))
| cyclefreeP(cons(skaf44(sk3),nil)) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) )
| ~ ssItem(skaf44(sk3))
| cyclefreeP(cons(skaf44(sk3),nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) )
| ~ ssItem(skaf44(sk3))
| cyclefreeP(cons(skaf44(sk3),nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) )
| ~ ssItem(skaf44(sk3))
| cyclefreeP(cons(skaf44(sk3),nil)) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
( ~ ssItem(skaf44(sk3))
| cyclefreeP(cons(skaf44(sk3),nil)) ),
inference(unit_resolution,[status(thm)],[153,150]) ).
tff(155,plain,
cyclefreeP(cons(skaf44(sk3),nil)),
inference(unit_resolution,[status(thm)],[154,143]) ).
tff(156,plain,
cyclefreeP(sk3),
inference(modus_ponens,[status(thm)],[155,134]) ).
tff(157,plain,
cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))),
inference(modus_ponens,[status(thm)],[156,113]) ).
tff(158,plain,
( ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(159,plain,
( ssList(sk3)
<=> ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))) ),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))),
inference(modus_ponens,[status(thm)],[119,159]) ).
tff(161,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| leq(U,U) )
<=> ( ~ ssItem(U)
| leq(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(162,plain,
( ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
( ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,axiom,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause62) ).
tff(165,plain,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
inference(skolemize,[status(sab)],[165]) ).
tff(167,plain,
! [U: $i] :
( ~ ssItem(U)
| leq(U,U) ),
inference(modus_ponens,[status(thm)],[166,162]) ).
tff(168,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk6)
| leq(sk6,sk6) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk6)
| leq(sk6,sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk6)
| leq(sk6,sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| leq(U,U) )
| ~ ssItem(sk6)
| leq(sk6,sk6) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
leq(sk6,sk6),
inference(unit_resolution,[status(thm)],[170,167,49]) ).
tff(172,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(173,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
rewrite(( ( ~ leq(U,V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(176,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ leq(U,V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ leq(U,V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ leq(U,V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(178,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ leq(U,V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(179,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ leq(U,V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) ),
inference(transitivity,[status(thm)],[178,177]) ).
tff(180,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) ),
inference(transitivity,[status(thm)],[179,176]) ).
tff(181,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z ) )
<=> ( ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y) )
<=> ( ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssList(Y) ) )),
rewrite(( ( ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssList(Y) )
<=> ( ~ ssList(Y)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y) )
<=> ( ~ ssList(Y)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X) )
<=> ( ~ ssList(Y)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssList(X) ) )),
rewrite(( ( ~ ssList(Y)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(Y)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(Y)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ~ ssList(Y)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssList(W) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(Y)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssList(X)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssItem(U) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| ~ cyclefreeP(Z) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ cyclefreeP(Z) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ cyclefreeP(Z) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| ~ cyclefreeP(Z) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| ~ cyclefreeP(Z)
| ~ ssList(Z) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssList(Z) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssList(Z) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| ~ cyclefreeP(Z)
| ~ ssList(Z) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| ~ cyclefreeP(Z)
| ~ ssList(Z) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ~ cyclefreeP(Z)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ leq(V,U)
| ~ leq(U,V) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| ~ cyclefreeP(Z)
| ~ ssList(Z) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ) ),
inference(transitivity,[status(thm)],[182,180]) ).
tff(184,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ leq(U,V)
| ~ leq(V,U)
| ( app(app(W,cons(U,X)),cons(V,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| ~ cyclefreeP(Z)
| ~ ssList(Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause185) ).
tff(185,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ),
inference(modus_ponens,[status(thm)],[185,174]) ).
tff(187,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ),
inference(skolemize,[status(sab)],[186]) ).
tff(188,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) ),
inference(modus_ponens,[status(thm)],[187,173]) ).
tff(189,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,plain,
( ( ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ leq(sk6,sk6) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(191,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ leq(sk6,sk6) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))) ) ),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ leq(sk6,sk6) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))) ) ),
inference(transitivity,[status(thm)],[191,189]) ).
tff(193,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ leq(sk6,sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ leq(U,V)
| ~ ssList(app(app(W,cons(U,X)),cons(V,Y)))
| ~ cyclefreeP(app(app(W,cons(U,X)),cons(V,Y)))
| ~ leq(V,U) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ leq(sk6,sk6)
| ~ ssList(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)))
| ~ cyclefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,sk8))) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
$false,
inference(unit_resolution,[status(thm)],[194,22,188,49,29,56,171,160,157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC166-1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 08:29:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.99/1.17 % SZS status Unsatisfiable
% 0.99/1.17 % SZS output start Proof
% See solution above
% 1.03/1.19 % E exiting
%------------------------------------------------------------------------------