%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC191-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:30:28 AM UTC 2025
% Result : Unsatisfiable 135.45s 135.70s
% Output : Proof 135.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 104
% Syntax : Number of formulae : 272 ( 92 unt; 0 typ; 0 def)
% Number of atoms : 1914 ( 517 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 2997 (1460 ~;1374 |; 0 &)
% ( 163 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 105 ( 105 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 568 ( 517 !; 0 ?; 568 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalelemsP_type,type,
equalelemsP: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf82_type,type,
skaf82: $i > $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(skaf83_type,type,
skaf83: $i > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(nil_type,type,
nil: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $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_14) ).
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_10) ).
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_12) ).
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_11) ).
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_13) ).
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,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(cons(sk5,nil),nil) = cons(sk5,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(cons(sk5,nil),nil) = cons(sk5,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(cons(sk5,nil),nil) = cons(sk5,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(cons(sk5,nil),nil) = cons(sk5,nil) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
app(cons(sk5,nil),nil) = cons(sk5,nil),
inference(unit_resolution,[status(thm)],[89,22,81,9]) ).
tff(91,plain,
app(sk7,app(cons(sk5,nil),nil)) = app(sk7,cons(sk5,nil)),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)),
inference(monotonicity,[status(thm)],[91,86]) ).
tff(93,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ssList(cons(sk6,sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ssList(cons(sk6,sk8)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ssList(cons(sk6,sk8)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ssList(cons(sk6,sk8)) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
ssList(cons(sk6,sk8)),
inference(unit_resolution,[status(thm)],[95,19,49,56]) ).
tff(97,plain,
( ssList(app(cons(sk5,nil),nil))
<=> ssList(cons(sk5,nil)) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(98,plain,
( ssList(cons(sk5,nil))
<=> ssList(app(cons(sk5,nil),nil)) ),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
ssList(app(cons(sk5,nil),nil)),
inference(modus_ponens,[status(thm)],[26,98]) ).
tff(100,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(cons(sk6,sk8))
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(cons(sk6,sk8))
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ssList(cons(sk6,sk8))
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(sk7)
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) )
<=> ( ~ ssList(sk7)
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(cons(sk6,sk8))
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk6,sk8))
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(sk7)
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(cons(sk6,sk8))
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk6,sk8))
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(sk7)
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(cons(sk6,sk8))
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) ) ),
inference(transitivity,[status(thm)],[102,100]) ).
tff(104,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk6,sk8))
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(sk7)
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(app(cons(sk5,nil),nil))
| ~ ssList(cons(sk6,sk8))
| ( app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))),
inference(unit_resolution,[status(thm)],[105,66,29,99,96]) ).
tff(107,plain,
app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))) = app(app(sk7,app(cons(sk5,nil),nil)),cons(sk6,sk8)),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
app(app(cons(sk5,nil),nil),cons(sk6,sk8)) = app(app(cons(sk5,nil),nil),app(cons(sk6,nil),sk8)),
inference(monotonicity,[status(thm)],[86]) ).
tff(109,plain,
app(app(cons(sk5,nil),nil),app(cons(sk6,nil),sk8)) = app(app(cons(sk5,nil),nil),cons(sk6,sk8)),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
app(sk7,app(app(cons(sk5,nil),nil),app(cons(sk6,nil),sk8))) = app(sk7,app(app(cons(sk5,nil),nil),cons(sk6,sk8))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
cons(sk5,nil) = app(cons(sk5,nil),nil),
inference(symmetry,[status(thm)],[90]) ).
tff(112,plain,
app(cons(sk5,nil),cons(sk6,sk8)) = app(app(cons(sk5,nil),nil),app(cons(sk6,nil),sk8)),
inference(monotonicity,[status(thm)],[111,86]) ).
tff(113,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,sk8))
| ( app(cons(sk5,nil),cons(sk6,sk8)) = cons(sk5,cons(sk6,sk8)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,sk8))
| ( app(cons(sk5,nil),cons(sk6,sk8)) = cons(sk5,cons(sk6,sk8)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,sk8))
| ( app(cons(sk5,nil),cons(sk6,sk8)) = cons(sk5,cons(sk6,sk8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,sk8))
| ( app(cons(sk5,nil),cons(sk6,sk8)) = cons(sk5,cons(sk6,sk8)) ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
app(cons(sk5,nil),cons(sk6,sk8)) = cons(sk5,cons(sk6,sk8)),
inference(unit_resolution,[status(thm)],[115,81,9,96]) ).
tff(117,plain,
cons(sk5,cons(sk6,sk8)) = app(cons(sk5,nil),cons(sk6,sk8)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ( nil = cons(sk6,sk8) )
<=> ( nil = app(cons(sk6,nil),sk8) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(119,plain,
( ( nil = app(cons(sk6,nil),sk8) )
<=> ( nil = cons(sk6,sk8) ) ),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ( nil != app(cons(sk6,nil),sk8) )
<=> ( nil != cons(sk6,sk8) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( ( app(cons(sk6,nil),sk8) = nil )
<=> ( nil = app(cons(sk6,nil),sk8) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(122,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(cons(sk6,nil),nil) = cons(sk6,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(cons(sk6,nil),nil) = cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(cons(sk6,nil),nil) = cons(sk6,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(cons(sk6,nil),nil) = cons(sk6,nil) ) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
app(cons(sk6,nil),nil) = cons(sk6,nil),
inference(unit_resolution,[status(thm)],[124,22,81,49]) ).
tff(126,plain,
app(app(cons(sk6,nil),nil),sk8) = app(cons(sk6,nil),sk8),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ( app(app(cons(sk6,nil),nil),sk8) = nil )
<=> ( app(cons(sk6,nil),sk8) = nil ) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ( app(app(cons(sk6,nil),nil),sk8) = nil )
<=> ( nil = app(cons(sk6,nil),sk8) ) ),
inference(transitivity,[status(thm)],[127,121]) ).
tff(129,plain,
( ( app(app(cons(sk6,nil),nil),sk8) != nil )
<=> ( nil != app(cons(sk6,nil),sk8) ) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ssList(app(cons(sk6,nil),nil))
<=> ssList(cons(sk6,nil)) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(131,plain,
( ssList(cons(sk6,nil))
<=> ssList(app(cons(sk6,nil),nil)) ),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
ssList(app(cons(sk6,nil),nil)),
inference(modus_ponens,[status(thm)],[53,131]) ).
tff(133,plain,
( ( nil = cons(sk6,nil) )
<=> ( cons(sk6,nil) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(134,plain,
( ( nil = app(cons(sk6,nil),nil) )
<=> ( nil = cons(sk6,nil) ) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(135,plain,
( ( nil = app(cons(sk6,nil),nil) )
<=> ( cons(sk6,nil) = nil ) ),
inference(transitivity,[status(thm)],[134,133]) ).
tff(136,plain,
( ( cons(sk6,nil) = nil )
<=> ( nil = app(cons(sk6,nil),nil) ) ),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ( cons(sk6,nil) != nil )
<=> ( nil != app(cons(sk6,nil),nil) ) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( cons(U,V) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(144,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[144,140]) ).
tff(146,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[145]) ).
tff(147,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[146,139]) ).
tff(148,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( cons(sk6,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( cons(sk6,nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( cons(sk6,nil) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( cons(sk6,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
cons(sk6,nil) != nil,
inference(unit_resolution,[status(thm)],[150,22,147,49]) ).
tff(152,plain,
nil != app(cons(sk6,nil),nil),
inference(modus_ponens,[status(thm)],[151,137]) ).
tff(153,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(154,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[153]) ).
tff(155,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(157,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
tff(159,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[159,155]) ).
tff(161,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(skolemize,[status(sab)],[160]) ).
tff(162,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[161,154]) ).
tff(163,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ( ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(sk8)
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) )
<=> ( ~ ssList(sk8)
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(sk8)
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) ) ),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(sk8)
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) ) ),
inference(transitivity,[status(thm)],[165,163]) ).
tff(167,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ~ ssList(sk8)
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk8)
| ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
( ~ ssList(app(cons(sk6,nil),nil))
| ( nil = app(cons(sk6,nil),nil) )
| ( app(app(cons(sk6,nil),nil),sk8) != nil ) ),
inference(unit_resolution,[status(thm)],[168,162,56]) ).
tff(170,plain,
app(app(cons(sk6,nil),nil),sk8) != nil,
inference(unit_resolution,[status(thm)],[169,152,132]) ).
tff(171,plain,
nil != app(cons(sk6,nil),sk8),
inference(modus_ponens,[status(thm)],[170,129]) ).
tff(172,plain,
nil != cons(sk6,sk8),
inference(modus_ponens,[status(thm)],[171,120]) ).
tff(173,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(174,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)],[173]) ).
tff(175,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(176,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(177,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)],[176]) ).
tff(178,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(179,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[179,175]) ).
tff(181,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[180]) ).
tff(182,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[181,174]) ).
tff(183,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(cons(sk6,sk8))
| ( nil = cons(sk6,sk8) )
| ( cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) = cons(sk6,sk8) ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(cons(sk6,sk8))
| ( nil = cons(sk6,sk8) )
| ( cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) = cons(sk6,sk8) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(cons(sk6,sk8))
| ( nil = cons(sk6,sk8) )
| ( cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) = cons(sk6,sk8) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(185,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(cons(sk6,sk8))
| ( nil = cons(sk6,sk8) )
| ( cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) = cons(sk6,sk8) ) ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) = cons(sk6,sk8),
inference(unit_resolution,[status(thm)],[185,182,96,172]) ).
tff(187,plain,
cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))) = cons(sk5,cons(sk6,sk8)),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))) = app(app(cons(sk5,nil),nil),app(cons(sk6,nil),sk8)),
inference(transitivity,[status(thm)],[187,117,112]) ).
tff(189,plain,
app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))) = app(sk7,app(app(cons(sk5,nil),nil),app(cons(sk6,nil),sk8))),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))) = sk3,
inference(transitivity,[status(thm)],[189,110,107,92,71,6,3]) ).
tff(191,plain,
( equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
<=> equalelemsP(sk3) ),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( equalelemsP(sk3)
<=> equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) ),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
( equalelemsP(sk3)
<=> equalelemsP(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(194,axiom,
equalelemsP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(195,plain,
equalelemsP(sk3),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))),
inference(modus_ponens,[status(thm)],[195,192]) ).
tff(197,plain,
^ [U: $i] :
refl(( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],[]) ).
tff(198,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[197]) ).
tff(199,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(200,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(201,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[201]) ).
tff(203,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[202,198]) ).
tff(204,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(cons(sk6,sk8))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,plain,
ssList(skaf82(cons(sk6,sk8))),
inference(unit_resolution,[status(thm)],[204,203]) ).
tff(206,plain,
^ [U: $i] :
refl(( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],[]) ).
tff(207,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[206]) ).
tff(208,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(210,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[210]) ).
tff(212,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[211,207]) ).
tff(213,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(cons(sk6,sk8))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
ssItem(skaf83(cons(sk6,sk8))),
inference(unit_resolution,[status(thm)],[213,212]) ).
tff(215,plain,
cons(sk6,sk8) = cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))),
inference(symmetry,[status(thm)],[186]) ).
tff(216,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(217,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[216]) ).
tff(218,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( U = W ) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( U = W ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(220,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[219]) ).
tff(221,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( U = W ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause170) ).
tff(222,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[222,218]) ).
tff(224,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(skolemize,[status(sab)],[223]) ).
tff(225,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[224,217]) ).
tff(226,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(227,plain,
( ( ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) )
<=> ( ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) ) ),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) ) ),
inference(transitivity,[status(thm)],[228,226]) ).
tff(230,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(231,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( U = W )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk6 = skaf83(cons(sk6,sk8)) )
| ( cons(sk6,sk8) != cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))) ) ),
inference(modus_ponens,[status(thm)],[230,229]) ).
tff(232,plain,
( ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk6 = skaf83(cons(sk6,sk8)) ) ),
inference(unit_resolution,[status(thm)],[231,225,49,56,215]) ).
tff(233,plain,
sk6 = skaf83(cons(sk6,sk8)),
inference(unit_resolution,[status(thm)],[232,214,205]) ).
tff(234,plain,
skaf83(cons(sk6,sk8)) = sk6,
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
( ( sk5 = skaf83(cons(sk6,sk8)) )
<=> ( sk5 = sk6 ) ),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
( ( sk5 = sk6 )
<=> ( sk5 = skaf83(cons(sk6,sk8)) ) ),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
( ( sk5 != sk6 )
<=> ( sk5 != skaf83(cons(sk6,sk8)) ) ),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
( ( sk5 != sk6 )
<=> ( sk5 != sk6 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(239,axiom,
sk5 != sk6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(240,plain,
sk5 != sk6,
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
sk5 != skaf83(cons(sk6,sk8)),
inference(modus_ponens,[status(thm)],[240,237]) ).
tff(242,plain,
( ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[190]) ).
tff(243,plain,
( ssList(sk3)
<=> ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) ),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(246,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))),
inference(modus_ponens,[status(thm)],[246,243]) ).
tff(248,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ) )),
inference(bind,[status(th)],[]) ).
tff(249,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ) ),
inference(quant_intro,[status(thm)],[248]) ).
tff(250,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(251,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X))))
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ) )),
inference(bind,[status(th)],[]) ).
tff(252,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X))))
| ~ ssItem(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ) ),
inference(quant_intro,[status(thm)],[251]) ).
tff(253,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X))))
| ~ ssItem(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X))))
| ~ ssItem(W) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(254,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X))))
| ~ ssItem(W) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(255,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X))))
| ~ ssItem(W) ) ),
inference(transitivity,[status(thm)],[254,253]) ).
tff(256,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ) ),
inference(transitivity,[status(thm)],[255,252]) ).
tff(257,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(X)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssItem(W) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ equalelemsP(Y) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ equalelemsP(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(Y) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| ( V = W ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ( V = W ) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ( V = W ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| ( V = W ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
inference(bind,[status(th)],[]) ).
tff(258,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| ( V = W ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| ( V = W ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ) ),
inference(transitivity,[status(thm)],[258,256]) ).
tff(260,axiom,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause180) ).
tff(261,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ),
inference(modus_ponens,[status(thm)],[261,250]) ).
tff(263,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ),
inference(skolemize,[status(sab)],[262]) ).
tff(264,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) ),
inference(modus_ponens,[status(thm)],[263,249]) ).
tff(265,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(266,plain,
( ( ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) )
<=> ( ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(267,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) ) ),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) ) ),
inference(transitivity,[status(thm)],[267,265]) ).
tff(269,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(270,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(app(U,cons(V,cons(W,X))))
| ( V = W )
| ~ equalelemsP(app(U,cons(V,cons(W,X)))) )
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(skaf82(cons(sk6,sk8)))
| ~ ssItem(skaf83(cons(sk6,sk8)))
| ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) ),
inference(modus_ponens,[status(thm)],[269,268]) ).
tff(271,plain,
( ( sk5 = skaf83(cons(sk6,sk8)) )
| ~ ssList(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8))))))
| ~ equalelemsP(app(sk7,cons(sk5,cons(skaf83(cons(sk6,sk8)),skaf82(cons(sk6,sk8)))))) ),
inference(unit_resolution,[status(thm)],[270,264,9,29,205,214]) ).
tff(272,plain,
$false,
inference(unit_resolution,[status(thm)],[271,247,241,196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC191-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 08:34:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 135.45/135.70 % SZS status Unsatisfiable
% 135.45/135.70 % SZS output start Proof
% See solution above
% 135.95/136.19 % E exiting
%------------------------------------------------------------------------------