%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC416-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:31:11 AM UTC 2025
% Result : Unsatisfiable 0.84s 1.00s
% Output : Proof 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 84
% Syntax : Number of formulae : 219 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 1492 ( 522 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 2280 (1097 ~;1052 |; 0 &)
% ( 131 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 90 ( 90 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 360 ( 322 !; 0 ?; 360 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(hd_type,type,
hd: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( neq(nil,sk4)
<=> neq(nil,sk2) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( neq(nil,sk2)
<=> neq(nil,sk4) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ~ neq(nil,sk2)
<=> ~ neq(nil,sk4) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(9,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(12,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[13,8]) ).
tff(15,plain,
( ( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk3) = sk4 ) )
<=> ( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk3) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( ( app(cons(sk5,nil),sk3) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk3) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
( ( app(cons(sk5,nil),sk3) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(18,plain,
( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk3) = sk4 ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk3) = sk4 ) ),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
app(cons(sk5,nil),sk3) = sk4,
inference(unit_resolution,[status(thm)],[19,14]) ).
tff(21,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(23,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(28,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[33,30,23]) ).
tff(35,plain,
app(cons(sk5,nil),app(nil,sk3)) = app(cons(sk5,nil),sk3),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(38,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[38,14]) ).
tff(40,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(41,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)],[40]) ).
tff(42,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(43,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(44,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)],[43]) ).
tff(45,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(46,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(52,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,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(54,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(55,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)],[54,53]) ).
tff(56,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[55,52,49,39]) ).
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/sandbox/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(nil)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ( ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) ) ),
inference(rewrite,[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(sk3)
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
app(app(cons(sk5,nil),nil),sk3) = app(cons(sk5,nil),app(nil,sk3)),
inference(unit_resolution,[status(thm)],[72,52,66,23,56]) ).
tff(74,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(76,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,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(78,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)],[77]) ).
tff(79,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(80,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(81,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)],[80]) ).
tff(82,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(83,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[85,78]) ).
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)],[89,52,86,39]) ).
tff(91,plain,
cons(sk5,nil) = app(cons(sk5,nil),nil),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(96,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
tff(98,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( hd(cons(sk5,nil)) = sk5 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( hd(cons(sk5,nil)) = sk5 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( hd(cons(sk5,nil)) = sk5 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( hd(cons(sk5,nil)) = sk5 ) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
hd(cons(sk5,nil)) = sk5,
inference(unit_resolution,[status(thm)],[104,52,101,39]) ).
tff(106,plain,
( ( nil = cons(sk5,nil) )
<=> ( cons(sk5,nil) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(107,plain,
( ( cons(sk5,nil) = nil )
<=> ( nil = cons(sk5,nil) ) ),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ( cons(sk5,nil) != nil )
<=> ( nil != cons(sk5,nil) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,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(110,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)],[109]) ).
tff(111,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(112,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(113,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)],[112]) ).
tff(114,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(115,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[117,110]) ).
tff(119,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
cons(sk5,nil) != nil,
inference(unit_resolution,[status(thm)],[121,52,118,39]) ).
tff(123,plain,
nil != cons(sk5,nil),
inference(modus_ponens,[status(thm)],[122,108]) ).
tff(124,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(125,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause123) ).
tff(130,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
inference(modus_ponens,[status(thm)],[132,125]) ).
tff(134,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( hd(app(cons(sk5,nil),sk3)) = hd(cons(sk5,nil)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( hd(app(cons(sk5,nil),sk3)) = hd(cons(sk5,nil)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( hd(app(cons(sk5,nil),sk3)) = hd(cons(sk5,nil)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( hd(app(cons(sk5,nil),sk3)) = hd(cons(sk5,nil)) ) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
( ( nil = cons(sk5,nil) )
| ( hd(app(cons(sk5,nil),sk3)) = hd(cons(sk5,nil)) ) ),
inference(unit_resolution,[status(thm)],[136,133,23,56]) ).
tff(138,plain,
hd(app(cons(sk5,nil),sk3)) = hd(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[137,123]) ).
tff(139,plain,
app(cons(sk5,nil),sk3) = sk2,
inference(transitivity,[status(thm)],[20,4]) ).
tff(140,plain,
hd(app(cons(sk5,nil),sk3)) = hd(sk2),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
hd(sk2) = hd(app(cons(sk5,nil),sk3)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
hd(sk2) = sk5,
inference(transitivity,[status(thm)],[141,138,105]) ).
tff(143,plain,
cons(hd(sk2),nil) = cons(sk5,nil),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
cons(hd(sk2),nil) = app(cons(sk5,nil),nil),
inference(transitivity,[status(thm)],[143,91]) ).
tff(145,plain,
app(cons(hd(sk2),nil),sk1) = app(app(cons(sk5,nil),nil),sk3),
inference(monotonicity,[status(thm)],[144,76]) ).
tff(146,plain,
app(cons(hd(sk2),nil),sk1) = sk2,
inference(transitivity,[status(thm)],[145,73,35,20,4]) ).
tff(147,plain,
( ssList(cons(hd(sk2),nil))
<=> ssList(cons(sk5,nil)) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(148,plain,
( ssList(cons(sk5,nil))
<=> ssList(cons(hd(sk2),nil)) ),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
ssList(cons(hd(sk2),nil)),
inference(modus_ponens,[status(thm)],[56,148]) ).
tff(150,plain,
hd(cons(sk5,nil)) = hd(app(cons(sk5,nil),sk3)),
inference(symmetry,[status(thm)],[138]) ).
tff(151,plain,
sk5 = hd(cons(sk5,nil)),
inference(symmetry,[status(thm)],[105]) ).
tff(152,plain,
sk5 = hd(sk2),
inference(transitivity,[status(thm)],[151,150,140]) ).
tff(153,plain,
( ssItem(sk5)
<=> ssItem(hd(sk2)) ),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
ssItem(hd(sk2)),
inference(modus_ponens,[status(thm)],[39,153]) ).
tff(155,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,axiom,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
tff(157,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
( ( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) )
<=> ( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,plain,
( ( ~ ssItem(hd(sk2))
| ~ neq(sk4,nil)
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ~ neq(nil,sk2)
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) )
<=> ( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(hd(sk2))
| ~ neq(sk4,nil)
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ~ neq(nil,sk2)
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) )
<=> ( ~ ssItem(hd(sk2))
| ~ neq(sk4,nil)
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ~ neq(nil,sk2)
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(161,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssItem(hd(sk2))
| ~ neq(sk4,nil)
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ~ neq(nil,sk2)
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(162,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) )
<=> ( ~ ssItem(hd(sk2))
| ~ neq(sk4,nil)
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ~ neq(nil,sk2)
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ) ),
inference(transitivity,[status(thm)],[161,160]) ).
tff(163,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) )
<=> ( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ) ),
inference(transitivity,[status(thm)],[162,159]) ).
tff(164,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( sk2 != A )
| ( app(B,sk1) != A ) ) )),
rewrite(( ( ~ ssList(A)
| ~ ssList(B)
| ( sk2 != A )
| ( app(B,sk1) != A ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( app(B,sk1) != A )
| ( sk2 != A )
| ~ ssItem(C) ) )),
rewrite(( ( ~ ssList(A)
| ~ ssList(B)
| ( app(B,sk1) != A )
| ( sk2 != A )
| ~ ssItem(C) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B ) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(B,sk1) != A )
| ( sk2 != A )
| ( cons(C,nil) != B ) ) )),
rewrite(( ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( app(B,sk1) != A )
| ( sk2 != A )
| ( cons(C,nil) != B ) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B ) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B )
| ( hd(sk2) != C ) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A )
| ( hd(sk2) != C ) ) )),
rewrite(( ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A )
| ( hd(sk2) != C ) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B )
| ( hd(sk2) != C ) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B )
| ( hd(sk2) != C )
| ~ neq(nil,sk2) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A )
| ~ neq(nil,sk2) ) )),
rewrite(( ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A )
| ~ neq(nil,sk2) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B )
| ( hd(sk2) != C )
| ~ neq(nil,sk2) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B )
| ( hd(sk2) != C )
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A )
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssItem(C)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A )
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B )
| ( hd(sk2) != C )
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) ) )),
inference(bind,[status(th)],[]) ).
tff(165,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B )
| ( hd(sk2) != C )
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssItem(C)
| ~ neq(sk4,nil)
| ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( hd(sk2) != C )
| ( cons(C,nil) != B )
| ( app(B,sk1) != A )
| ( sk2 != A ) ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B )
| ( hd(sk2) != C )
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ) ),
inference(transitivity,[status(thm)],[165,163]) ).
tff(167,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( app(B,sk1) != A )
| ~ ssItem(C)
| ( cons(C,nil) != B )
| ( hd(sk2) != C )
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(168,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ),
inference(modus_ponens,[status(thm)],[168,158]) ).
tff(170,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ),
inference(modus_ponens,[status(thm)],[169,158]) ).
tff(171,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ),
inference(modus_ponens,[status(thm)],[170,158]) ).
tff(172,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ),
inference(modus_ponens,[status(thm)],[171,158]) ).
tff(173,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ( app(cons(hd(sk2),nil),sk1) != sk2 ) ),
inference(unit_resolution,[status(thm)],[172,157]) ).
tff(174,plain,
~ neq(nil,sk2),
inference(unit_resolution,[status(thm)],[173,154,14,149,146]) ).
tff(175,plain,
~ neq(nil,sk4),
inference(modus_ponens,[status(thm)],[174,7]) ).
tff(176,plain,
( ( sk4 = nil )
<=> ( nil = sk4 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(177,plain,
( ( app(cons(sk5,nil),sk3) = nil )
<=> ( sk4 = nil ) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(178,plain,
( ( app(cons(sk5,nil),sk3) = nil )
<=> ( nil = sk4 ) ),
inference(transitivity,[status(thm)],[177,176]) ).
tff(179,plain,
( ( app(cons(sk5,nil),sk3) != nil )
<=> ( nil != sk4 ) ),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,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(181,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)],[180]) ).
tff(182,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(183,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(184,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)],[183]) ).
tff(185,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
tff(186,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[186,182]) ).
tff(188,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(skolemize,[status(sab)],[187]) ).
tff(189,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[188,181]) ).
tff(190,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( app(cons(sk5,nil),sk3) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( app(cons(sk5,nil),sk3) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(191,plain,
( ( ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ~ ssList(sk3)
| ( app(cons(sk5,nil),sk3) != nil ) )
<=> ( ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( app(cons(sk5,nil),sk3) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ~ ssList(sk3)
| ( app(cons(sk5,nil),sk3) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( app(cons(sk5,nil),sk3) != nil ) ) ),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ~ ssList(sk3)
| ( app(cons(sk5,nil),sk3) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( app(cons(sk5,nil),sk3) != nil ) ) ),
inference(transitivity,[status(thm)],[192,190]) ).
tff(194,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ~ ssList(sk3)
| ( app(cons(sk5,nil),sk3) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ( nil = cons(sk5,nil) )
| ( app(cons(sk5,nil),sk3) != nil ) ),
inference(modus_ponens,[status(thm)],[194,193]) ).
tff(196,plain,
( ( nil = cons(sk5,nil) )
| ( app(cons(sk5,nil),sk3) != nil ) ),
inference(unit_resolution,[status(thm)],[195,189,23,56]) ).
tff(197,plain,
app(cons(sk5,nil),sk3) != nil,
inference(unit_resolution,[status(thm)],[196,123]) ).
tff(198,plain,
nil != sk4,
inference(modus_ponens,[status(thm)],[197,179]) ).
tff(199,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(200,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(201,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(203,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[202]) ).
tff(204,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(206,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[205]) ).
tff(207,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(208,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[208,204]) ).
tff(210,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[209]) ).
tff(211,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[210,203]) ).
tff(212,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 )
| neq(nil,sk4) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 )
| neq(nil,sk4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,plain,
( ( ~ ssList(sk4)
| ~ ssList(nil)
| ( nil = sk4 )
| neq(nil,sk4) )
<=> ( ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 )
| neq(nil,sk4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( nil = sk4 )
| neq(nil,sk4) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 )
| neq(nil,sk4) ) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( nil = sk4 )
| neq(nil,sk4) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 )
| neq(nil,sk4) ) ),
inference(transitivity,[status(thm)],[214,212]) ).
tff(216,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( nil = sk4 )
| neq(nil,sk4) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 )
| neq(nil,sk4) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
neq(nil,sk4),
inference(unit_resolution,[status(thm)],[217,52,211,201,198]) ).
tff(219,plain,
$false,
inference(unit_resolution,[status(thm)],[218,175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWC416-1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 09:16:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.84/1.00 % SZS status Unsatisfiable
% 0.84/1.00 % SZS output start Proof
% See solution above
% 0.84/1.03 % E exiting
%------------------------------------------------------------------------------