%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC152-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:30:20 AM UTC 2025
% Result : Unsatisfiable 8.06s 8.24s
% Output : Proof 8.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 122
% Syntax : Number of formulae : 297 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 2427 ( 426 equ)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 3936 (1945 ~;1785 |; 0 &)
% ( 206 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 139 ( 139 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 678 ( 618 !; 0 ?; 678 :)
% Comments :
%------------------------------------------------------------------------------
tff(strictorderedP_type,type,
strictorderedP: $i > $o ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk11_type,type,
sk11: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk9_type,type,
sk9: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(1,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(4,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1 )
<=> ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(7,plain,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk3,
inference(transitivity,[status(thm)],[7,4]) ).
tff(9,plain,
( ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[9,1]) ).
tff(11,plain,
( ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
<=> ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(13,plain,
( ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) = nil )
<=> ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) ) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
<=> ( nil != app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) ) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ( nil = cons(sk6,nil) )
<=> ( cons(sk6,nil) = nil ) ),
inference(commutativity,[status(thm)],[]) ).
tff(16,plain,
( ( cons(sk6,nil) = nil )
<=> ( nil = cons(sk6,nil) ) ),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( ( cons(sk6,nil) != nil )
<=> ( nil != cons(sk6,nil) ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(20,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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(25,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)],[24]) ).
tff(26,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(27,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(33,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,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(35,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(36,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)],[35,34]) ).
tff(37,plain,
cons(sk6,nil) != nil,
inference(unit_resolution,[status(thm)],[36,33,30,20]) ).
tff(38,plain,
nil != cons(sk6,nil),
inference(modus_ponens,[status(thm)],[37,17]) ).
tff(39,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(41,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,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(43,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)],[42]) ).
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(rewrite,[status(thm)],[]) ).
tff(45,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(46,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)],[45]) ).
tff(47,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(48,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,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(53,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(54,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)],[53,52]) ).
tff(55,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[54,33,51,41]) ).
tff(56,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(58,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,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(63,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)],[62]) ).
tff(64,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(65,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,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(70,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(71,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)],[70]) ).
tff(72,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)],[71,69]) ).
tff(73,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(74,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)],[73,72]) ).
tff(75,plain,
ssList(app(sk7,cons(sk5,nil))),
inference(unit_resolution,[status(thm)],[74,68,58,55]) ).
tff(76,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(78,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ssList(app(app(sk7,cons(sk5,nil)),sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ssList(app(app(sk7,cons(sk5,nil)),sk8)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ ssList(sk8)
| ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ~ ssList(app(sk7,cons(sk5,nil))) )
<=> ( ~ ssList(sk8)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ssList(app(app(sk7,cons(sk5,nil)),sk8)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ~ ssList(app(sk7,cons(sk5,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ssList(app(app(sk7,cons(sk5,nil)),sk8)) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ~ ssList(app(sk7,cons(sk5,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ssList(app(app(sk7,cons(sk5,nil)),sk8)) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ~ ssList(app(sk7,cons(sk5,nil))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ssList(app(app(sk7,cons(sk5,nil)),sk8)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
ssList(app(app(sk7,cons(sk5,nil)),sk8)),
inference(unit_resolution,[status(thm)],[84,68,78,75]) ).
tff(86,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(87,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(88,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)],[87,86]) ).
tff(89,plain,
ssList(cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[88,33,51,20]) ).
tff(90,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
tff(96,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ~ ssList(cons(sk6,nil))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) )
<=> ( ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ~ ssList(cons(sk6,nil))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ~ ssList(cons(sk6,nil))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ) ),
inference(transitivity,[status(thm)],[102,100]) ).
tff(104,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ~ ssList(cons(sk6,nil))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
( ( app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil )
| ( nil = cons(sk6,nil) ) ),
inference(unit_resolution,[status(thm)],[105,99,89,85]) ).
tff(107,plain,
app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) != nil,
inference(unit_resolution,[status(thm)],[106,38]) ).
tff(108,plain,
nil != app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),
inference(modus_ponens,[status(thm)],[107,14]) ).
tff(109,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( ~ ssList(cons(sk6,nil))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8)) )
<=> ( ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil))) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil))) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil))) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil))),
inference(unit_resolution,[status(thm)],[114,68,89,85]) ).
tff(116,plain,
( ssList(sk9)
<=> ssList(sk9) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
ssList(sk9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(118,plain,
ssList(sk9),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,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(120,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)],[119]) ).
tff(121,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(122,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(123,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)],[122]) ).
tff(124,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(125,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[127,120]) ).
tff(129,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk9)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk9)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ( ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ~ ssList(sk9)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) )
<=> ( ~ ssList(sk9)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ~ ssList(sk9)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk9)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ~ ssList(sk9)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk9)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ~ ssList(sk9)
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk9)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)))
| ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( ( nil = app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)) )
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil ) ),
inference(unit_resolution,[status(thm)],[134,128,118,115]) ).
tff(136,plain,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) != nil,
inference(unit_resolution,[status(thm)],[135,108]) ).
tff(137,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[136,11]) ).
tff(138,plain,
( ( ( nil = sk3 )
| ( cons(sk11,nil) = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk11,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
( ( ( cons(sk11,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk11,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,axiom,
( ( cons(sk11,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_22) ).
tff(141,plain,
( ( nil = sk3 )
| ( cons(sk11,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
( ( nil = sk3 )
| ( cons(sk11,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[141,138]) ).
tff(143,plain,
cons(sk11,nil) = sk3,
inference(unit_resolution,[status(thm)],[142,137]) ).
tff(144,plain,
( strictorderedP(cons(sk11,nil))
<=> strictorderedP(sk3) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( strictorderedP(sk3)
<=> strictorderedP(cons(sk11,nil)) ),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ~ strictorderedP(sk3)
<=> ~ strictorderedP(cons(sk11,nil)) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,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(148,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)],[147]) ).
tff(149,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(150,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(151,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)],[150]) ).
tff(152,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(153,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)],[152,151]) ).
tff(154,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)],[153,149]) ).
tff(155,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)],[154]) ).
tff(156,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)],[155,148]) ).
tff(157,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = app(app(app(sk7,cons(sk5,nil)),sk8),app(cons(sk6,nil),sk9)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = app(app(app(sk7,cons(sk5,nil)),sk8),app(cons(sk6,nil),sk9)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = app(app(app(sk7,cons(sk5,nil)),sk8),app(cons(sk6,nil),sk9)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),sk8))
| ( app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = app(app(app(sk7,cons(sk5,nil)),sk8),app(cons(sk6,nil),sk9)) ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = app(app(app(sk7,cons(sk5,nil)),sk8),app(cons(sk6,nil),sk9)),
inference(unit_resolution,[status(thm)],[159,156,118,89,85]) ).
tff(161,plain,
app(app(app(sk7,cons(sk5,nil)),sk8),app(cons(sk6,nil),sk9)) = app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),
inference(symmetry,[status(thm)],[160]) ).
tff(162,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(163,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)],[162]) ).
tff(164,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(165,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(166,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)],[165]) ).
tff(167,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(168,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[169]) ).
tff(171,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[170,163]) ).
tff(172,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk9)
| ( app(cons(sk6,nil),sk9) = cons(sk6,sk9) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk9)
| ( app(cons(sk6,nil),sk9) = cons(sk6,sk9) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk9)
| ( app(cons(sk6,nil),sk9) = cons(sk6,sk9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk9)
| ( app(cons(sk6,nil),sk9) = cons(sk6,sk9) ) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
app(cons(sk6,nil),sk9) = cons(sk6,sk9),
inference(unit_resolution,[status(thm)],[174,171,20,118]) ).
tff(176,plain,
cons(sk6,sk9) = app(cons(sk6,nil),sk9),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,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(cons(sk5,nil))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,nil),sk8)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
( ( ~ ssList(sk8)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,nil),sk8)) ) )
<=> ( ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,nil),sk8)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(179,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(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,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(cons(sk5,nil))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,nil),sk8)) ) ) ),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,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(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,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(cons(sk5,nil))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,nil),sk8)) ) ) ),
inference(transitivity,[status(thm)],[179,177]) ).
tff(181,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(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,nil),sk8)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(182,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,nil),sk8)) ) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
app(app(sk7,cons(sk5,nil)),sk8) = app(sk7,app(cons(sk5,nil),sk8)),
inference(unit_resolution,[status(thm)],[182,156,58,78,55]) ).
tff(184,plain,
app(sk7,app(cons(sk5,nil),sk8)) = app(app(sk7,cons(sk5,nil)),sk8),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ( app(cons(sk5,nil),sk8) = cons(sk5,sk8) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ( app(cons(sk5,nil),sk8) = cons(sk5,sk8) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ( app(cons(sk5,nil),sk8) = cons(sk5,sk8) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ( app(cons(sk5,nil),sk8) = cons(sk5,sk8) ) ),
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
app(cons(sk5,nil),sk8) = cons(sk5,sk8),
inference(unit_resolution,[status(thm)],[187,171,41,78]) ).
tff(189,plain,
cons(sk5,sk8) = app(cons(sk5,nil),sk8),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
app(sk7,cons(sk5,sk8)) = app(sk7,app(cons(sk5,nil),sk8)),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
app(sk7,cons(sk5,sk8)) = app(app(sk7,cons(sk5,nil)),sk8),
inference(transitivity,[status(thm)],[190,184]) ).
tff(192,plain,
app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)) = app(app(app(sk7,cons(sk5,nil)),sk8),app(cons(sk6,nil),sk9)),
inference(monotonicity,[status(thm)],[191,176]) ).
tff(193,plain,
app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)) = sk3,
inference(transitivity,[status(thm)],[192,161,7,4]) ).
tff(194,plain,
( strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
<=> strictorderedP(sk3) ),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
( ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
<=> ~ strictorderedP(sk3) ),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
( ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[193]) ).
tff(197,plain,
( ssList(sk3)
<=> ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) ),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(199,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(200,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))),
inference(modus_ponens,[status(thm)],[200,197]) ).
tff(202,plain,
^ [V: $i] :
refl(( ( ~ ssItem(V)
| ~ lt(V,V) )
<=> ( ~ ssItem(V)
| ~ lt(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(203,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(quant_intro,[status(thm)],[202]) ).
tff(204,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,plain,
^ [V: $i] :
rewrite(( ( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ( ~ ssItem(V)
| ~ lt(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(206,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(quant_intro,[status(thm)],[205]) ).
tff(207,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(208,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(209,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(transitivity,[status(thm)],[208,207]) ).
tff(210,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(transitivity,[status(thm)],[209,206]) ).
tff(211,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
( ( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ( U != V )
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ lt(U,V)
| ( U != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
( ( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(212,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) ),
inference(quant_intro,[status(thm)],[211]) ).
tff(213,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(transitivity,[status(thm)],[212,210]) ).
tff(214,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause111) ).
tff(215,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[215,204]) ).
tff(217,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(skolemize,[status(sab)],[216]) ).
tff(218,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[217,203]) ).
tff(219,plain,
( ( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk6)
| ~ lt(sk6,sk6) )
<=> ( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk6)
| ~ lt(sk6,sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk6)
| ~ lt(sk6,sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk6)
| ~ lt(sk6,sk6) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
~ lt(sk6,sk6),
inference(unit_resolution,[status(thm)],[221,218,20]) ).
tff(223,plain,
( leq(sk6,sk5)
<=> leq(sk6,sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(224,axiom,
leq(sk6,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(225,plain,
leq(sk6,sk5),
inference(modus_ponens,[status(thm)],[224,223]) ).
tff(226,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(227,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ) ),
inference(quant_intro,[status(thm)],[226]) ).
tff(228,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(229,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W) )
<=> ( ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W) ) )),
( ( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V) )
<=> ( ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W)
| ~ ssItem(V) ) )),
rewrite(( ( ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W) ) )),
( ( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W) ) )),
( ( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W) ) )),
( ( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W) ) )),
( ( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,W) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W)
| lt(U,W) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| ~ lt(V,W)
| lt(U,W) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ) )),
( ( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,W) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(230,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ) ),
inference(quant_intro,[status(thm)],[229]) ).
tff(231,axiom,
! [W: $i,V: $i,U: $i] :
( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause147) ).
tff(232,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ),
inference(modus_ponens,[status(thm)],[232,228]) ).
tff(234,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ),
inference(skolemize,[status(sab)],[233]) ).
tff(235,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) ),
inference(modus_ponens,[status(thm)],[234,227]) ).
tff(236,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ leq(sk6,sk5)
| ~ lt(sk5,sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ leq(sk6,sk5)
| ~ lt(sk5,sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(237,plain,
( ( ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ lt(sk5,sk6) )
<=> ( ~ ssItem(sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ leq(sk6,sk5)
| ~ lt(sk5,sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(238,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ lt(sk5,sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ leq(sk6,sk5)
| ~ lt(sk5,sk6) ) ),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ lt(sk5,sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ leq(sk6,sk5)
| ~ lt(sk5,sk6) ) ),
inference(transitivity,[status(thm)],[238,236]) ).
tff(240,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ lt(sk5,sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ leq(sk6,sk5)
| ~ lt(sk5,sk6) ),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
~ lt(sk5,sk6),
inference(unit_resolution,[status(thm)],[241,235,41,20,225,222]) ).
tff(243,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) )),
inference(bind,[status(th)],[]) ).
tff(244,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(quant_intro,[status(thm)],[243]) ).
tff(245,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(246,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) )),
inference(bind,[status(th)],[]) ).
tff(247,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(quant_intro,[status(thm)],[246]) ).
tff(248,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(249,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(250,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssList(W) ) ),
inference(transitivity,[status(thm)],[249,248]) ).
tff(251,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(transitivity,[status(thm)],[250,247]) ).
tff(252,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y) )
<=> ( ~ ssList(Y)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W) )
<=> ( ~ ssList(Y)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(W) ) )),
rewrite(( ( ~ ssList(Y)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(W) )
<=> ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W) )
<=> ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X) )
<=> ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(X) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(V) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ strictorderedP(Z) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ strictorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Z) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| lt(V,X) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| lt(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(253,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ),
inference(quant_intro,[status(thm)],[252]) ).
tff(254,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ) ),
inference(transitivity,[status(thm)],[253,251]) ).
tff(255,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause181) ).
tff(256,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ),
inference(modus_ponens,[status(thm)],[256,245]) ).
tff(258,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ),
inference(skolemize,[status(sab)],[257]) ).
tff(259,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) ),
inference(modus_ponens,[status(thm)],[258,244]) ).
tff(260,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| lt(sk5,sk6)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| lt(sk5,sk6)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(261,plain,
( ( ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| lt(sk5,sk6)
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) )
<=> ( ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| lt(sk5,sk6)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(262,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| lt(sk5,sk6)
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| lt(sk5,sk6)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) ) ),
inference(monotonicity,[status(thm)],[261]) ).
tff(263,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| lt(sk5,sk6)
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| lt(sk5,sk6)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) ) ),
inference(transitivity,[status(thm)],[262,260]) ).
tff(264,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| lt(sk5,sk6)
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(265,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| lt(V,X)
| ~ strictorderedP(app(app(U,cons(V,W)),cons(X,Y))) )
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| lt(sk5,sk6)
| ~ ssList(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9)))
| ~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))) ),
inference(modus_ponens,[status(thm)],[264,263]) ).
tff(266,plain,
~ strictorderedP(app(app(sk7,cons(sk5,sk8)),cons(sk6,sk9))),
inference(unit_resolution,[status(thm)],[265,259,41,20,58,78,118,242,201]) ).
tff(267,plain,
~ strictorderedP(sk3),
inference(modus_ponens,[status(thm)],[266,195]) ).
tff(268,plain,
~ strictorderedP(cons(sk11,nil)),
inference(modus_ponens,[status(thm)],[267,146]) ).
tff(269,plain,
( ( ssItem(sk11)
| ( nil = sk3 ) )
<=> ( ssItem(sk11)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(270,axiom,
( ssItem(sk11)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
tff(271,plain,
( ssItem(sk11)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
ssItem(sk11),
inference(unit_resolution,[status(thm)],[271,137]) ).
tff(273,plain,
^ [V: $i] :
refl(( ( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
<=> ( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ) )),
inference(bind,[status(th)],[]) ).
tff(274,plain,
( ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
<=> ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ) ),
inference(quant_intro,[status(thm)],[273]) ).
tff(275,plain,
( ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
<=> ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(276,plain,
^ [V: $i] :
rewrite(( ( strictorderedP(cons(V,nil))
| ~ ssList(nil)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ) )),
inference(bind,[status(th)],[]) ).
tff(277,plain,
( ! [V: $i] :
( strictorderedP(cons(V,nil))
| ~ ssList(nil)
| ~ ssItem(V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ) ),
inference(quant_intro,[status(thm)],[276]) ).
tff(278,plain,
( ! [V: $i,U: $i] :
( strictorderedP(cons(V,nil))
| ~ ssList(nil)
| ~ ssItem(V) )
<=> ! [V: $i] :
( strictorderedP(cons(V,nil))
| ~ ssList(nil)
| ~ ssItem(V) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(279,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i,U: $i] :
( strictorderedP(cons(V,nil))
| ~ ssList(nil)
| ~ ssItem(V) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(280,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i] :
( strictorderedP(cons(V,nil))
| ~ ssList(nil)
| ~ ssItem(V) ) ),
inference(transitivity,[status(thm)],[279,278]) ).
tff(281,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ) ),
inference(transitivity,[status(thm)],[280,277]) ).
tff(282,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( nil != U )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U ) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
rewrite(( ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
inference(bind,[status(th)],[]) ).
tff(283,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) ),
inference(quant_intro,[status(thm)],[282]) ).
tff(284,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ) ),
inference(transitivity,[status(thm)],[283,281]) ).
tff(285,axiom,
! [V: $i,U: $i] :
( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause112) ).
tff(286,plain,
! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ),
inference(modus_ponens,[status(thm)],[285,284]) ).
tff(287,plain,
! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ),
inference(modus_ponens,[status(thm)],[286,275]) ).
tff(288,plain,
! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ),
inference(skolemize,[status(sab)],[287]) ).
tff(289,plain,
! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) ),
inference(modus_ponens,[status(thm)],[288,274]) ).
tff(290,plain,
( ( ~ ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
| ~ ssList(nil)
| ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil)) )
<=> ( ~ ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
| ~ ssList(nil)
| ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(291,plain,
( ( ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil))
| ~ ssList(nil) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(292,plain,
( ( ~ ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
| ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
| ~ ssList(nil)
| ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil)) ) ),
inference(monotonicity,[status(thm)],[291]) ).
tff(293,plain,
( ( ~ ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
| ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
| ~ ssList(nil)
| ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil)) ) ),
inference(transitivity,[status(thm)],[292,290]) ).
tff(294,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
| ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil))
| ~ ssList(nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| strictorderedP(cons(V,nil))
| ~ ssList(nil) )
| ~ ssList(nil)
| ~ ssItem(sk11)
| strictorderedP(cons(sk11,nil)) ),
inference(modus_ponens,[status(thm)],[294,293]) ).
tff(296,plain,
strictorderedP(cons(sk11,nil)),
inference(unit_resolution,[status(thm)],[295,33,289,272]) ).
tff(297,plain,
$false,
inference(unit_resolution,[status(thm)],[296,268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC152-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 08:26:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 8.06/8.24 % SZS status Unsatisfiable
% 8.06/8.24 % SZS output start Proof
% See solution above
% 8.09/8.31 % E exiting
%------------------------------------------------------------------------------