%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC303-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:30:51 AM UTC 2025
% Result : Unsatisfiable 1.30s 1.46s
% Output : Proof 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 89
% Syntax : Number of formulae : 212 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 1755 ( 204 equ)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 2842 (1395 ~;1310 |; 0 &)
% ( 137 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 96 ( 96 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 513 ( 467 !; 0 ?; 513 :)
% Comments :
%------------------------------------------------------------------------------
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(sk7_type,type,
sk7: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(totalorderedP_type,type,
totalorderedP: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk10_type,type,
sk10: $i ).
tff(sk9_type,type,
sk9: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(nil_type,type,
nil: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( sk3 = sk1 )
<=> ( sk3 = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk3 = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk3 = sk1,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk1 = sk3,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10) = sk1 )
<=> ( app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10) = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(7,plain,
app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10) = sk1,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(10,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,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(12,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,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(14,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(15,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)],[14]) ).
tff(16,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(17,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(23,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,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(25,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(26,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)],[25,24]) ).
tff(27,plain,
ssList(cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[26,23,20,10]) ).
tff(28,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(30,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,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(32,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,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(34,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(35,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)],[34]) ).
tff(36,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ssList(app(sk8,cons(sk6,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ssList(app(sk8,cons(sk6,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil)))
| ~ ssList(sk8) )
<=> ( ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ssList(app(sk8,cons(sk6,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil)))
| ~ ssList(sk8) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ssList(app(sk8,cons(sk6,nil))) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil)))
| ~ ssList(sk8) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ssList(app(sk8,cons(sk6,nil))) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil)))
| ~ ssList(sk8) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ssList(app(sk8,cons(sk6,nil))) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
ssList(app(sk8,cons(sk6,nil))),
inference(unit_resolution,[status(thm)],[46,40,30,27]) ).
tff(48,plain,
( ssList(sk9)
<=> ssList(sk9) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
ssList(sk9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(50,plain,
ssList(sk9),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ~ ssList(app(sk8,cons(sk6,nil)))
| ssList(app(app(sk8,cons(sk6,nil)),sk9)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ~ ssList(app(sk8,cons(sk6,nil)))
| ssList(app(app(sk8,cons(sk6,nil)),sk9)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ssList(sk9)
| ssList(app(app(sk8,cons(sk6,nil)),sk9))
| ~ ssList(app(sk8,cons(sk6,nil))) )
<=> ( ~ ssList(sk9)
| ~ ssList(app(sk8,cons(sk6,nil)))
| ssList(app(app(sk8,cons(sk6,nil)),sk9)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ssList(app(app(sk8,cons(sk6,nil)),sk9))
| ~ ssList(app(sk8,cons(sk6,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ~ ssList(app(sk8,cons(sk6,nil)))
| ssList(app(app(sk8,cons(sk6,nil)),sk9)) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ssList(app(app(sk8,cons(sk6,nil)),sk9))
| ~ ssList(app(sk8,cons(sk6,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ~ ssList(app(sk8,cons(sk6,nil)))
| ssList(app(app(sk8,cons(sk6,nil)),sk9)) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ssList(app(app(sk8,cons(sk6,nil)),sk9))
| ~ ssList(app(sk8,cons(sk6,nil))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ~ ssList(app(sk8,cons(sk6,nil)))
| ssList(app(app(sk8,cons(sk6,nil)),sk9)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
ssList(app(app(sk8,cons(sk6,nil)),sk9)),
inference(unit_resolution,[status(thm)],[56,40,50,47]) ).
tff(58,plain,
( ssItem(sk7)
<=> ssItem(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
ssItem(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(60,plain,
ssItem(sk7),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
ssList(cons(sk7,nil)),
inference(unit_resolution,[status(thm)],[63,23,20,60]) ).
tff(65,plain,
( ssList(sk10)
<=> ssList(sk10) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
ssList(sk10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(67,plain,
ssList(sk10),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,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(69,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)],[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)) ) )
<=> ! [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(71,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(72,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)],[71]) ).
tff(73,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(74,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)],[73,72]) ).
tff(75,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)],[74,70]) ).
tff(76,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)],[75]) ).
tff(77,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)],[76,69]) ).
tff(78,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(app(app(sk8,cons(sk6,nil)),sk9))
| ( app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10) = app(app(app(sk8,cons(sk6,nil)),sk9),app(cons(sk7,nil),sk10)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(app(app(sk8,cons(sk6,nil)),sk9))
| ( app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10) = app(app(app(sk8,cons(sk6,nil)),sk9),app(cons(sk7,nil),sk10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(app(app(sk8,cons(sk6,nil)),sk9))
| ( app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10) = app(app(app(sk8,cons(sk6,nil)),sk9),app(cons(sk7,nil),sk10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(app(app(sk8,cons(sk6,nil)),sk9))
| ( app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10) = app(app(app(sk8,cons(sk6,nil)),sk9),app(cons(sk7,nil),sk10)) ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10) = app(app(app(sk8,cons(sk6,nil)),sk9),app(cons(sk7,nil),sk10)),
inference(unit_resolution,[status(thm)],[80,77,67,64,57]) ).
tff(82,plain,
app(app(app(sk8,cons(sk6,nil)),sk9),app(cons(sk7,nil),sk10)) = app(app(app(app(sk8,cons(sk6,nil)),sk9),cons(sk7,nil)),sk10),
inference(symmetry,[status(thm)],[81]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,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(87,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)],[86]) ).
tff(88,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(89,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(cons(sk7,nil),sk10) = cons(sk7,sk10) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(cons(sk7,nil),sk10) = cons(sk7,sk10) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(cons(sk7,nil),sk10) = cons(sk7,sk10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(cons(sk7,nil),sk10) = cons(sk7,sk10) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
app(cons(sk7,nil),sk10) = cons(sk7,sk10),
inference(unit_resolution,[status(thm)],[95,92,60,67]) ).
tff(97,plain,
cons(sk7,sk10) = app(cons(sk7,nil),sk10),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(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(cons(sk6,nil))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(sk8,app(cons(sk6,nil),sk9)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ( ~ ssList(sk9)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(sk8,app(cons(sk6,nil),sk9)) ) )
<=> ( ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(sk8,app(cons(sk6,nil),sk9)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(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(cons(sk6,nil))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(sk8,app(cons(sk6,nil),sk9)) ) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,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(sk8)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(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(cons(sk6,nil))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(sk8,app(cons(sk6,nil),sk9)) ) ) ),
inference(transitivity,[status(thm)],[100,98]) ).
tff(102,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(sk8,app(cons(sk6,nil),sk9)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ( app(app(sk8,cons(sk6,nil)),sk9) = app(sk8,app(cons(sk6,nil),sk9)) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
app(app(sk8,cons(sk6,nil)),sk9) = app(sk8,app(cons(sk6,nil),sk9)),
inference(unit_resolution,[status(thm)],[103,77,30,50,27]) ).
tff(105,plain,
app(sk8,app(cons(sk6,nil),sk9)) = app(app(sk8,cons(sk6,nil)),sk9),
inference(symmetry,[status(thm)],[104]) ).
tff(106,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(107,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(108,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)],[107,106]) ).
tff(109,plain,
app(cons(sk6,nil),sk9) = cons(sk6,sk9),
inference(unit_resolution,[status(thm)],[108,92,10,50]) ).
tff(110,plain,
cons(sk6,sk9) = app(cons(sk6,nil),sk9),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
app(sk8,cons(sk6,sk9)) = app(sk8,app(cons(sk6,nil),sk9)),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
app(sk8,cons(sk6,sk9)) = app(app(sk8,cons(sk6,nil)),sk9),
inference(transitivity,[status(thm)],[111,105]) ).
tff(113,plain,
app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)) = app(app(app(sk8,cons(sk6,nil)),sk9),app(cons(sk7,nil),sk10)),
inference(monotonicity,[status(thm)],[112,97]) ).
tff(114,plain,
app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)) = sk3,
inference(transitivity,[status(thm)],[113,82,7,4]) ).
tff(115,plain,
( totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
<=> totalorderedP(sk3) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( totalorderedP(sk3)
<=> totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))) ),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
( totalorderedP(sk3)
<=> totalorderedP(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,axiom,
totalorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(119,plain,
totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))),
inference(modus_ponens,[status(thm)],[119,116]) ).
tff(121,plain,
app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)) = sk1,
inference(transitivity,[status(thm)],[113,82,7]) ).
tff(122,plain,
( ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
<=> ssList(sk1) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ssList(sk1)
<=> ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))) ),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(126,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))),
inference(modus_ponens,[status(thm)],[126,123]) ).
tff(128,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ) )),
inference(bind,[status(th)],[]) ).
tff(129,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
rewrite(( ( ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| leq(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ) )),
inference(bind,[status(th)],[]) ).
tff(132,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| leq(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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| leq(V,X) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| leq(V,X) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(134,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| leq(V,X) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(135,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(app(app(U,cons(V,W)),cons(X,Y)))
| ~ ssItem(V)
| ~ ssList(W)
| leq(V,X) ) ),
inference(transitivity,[status(thm)],[134,133]) ).
tff(136,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ) ),
inference(transitivity,[status(thm)],[135,132]) ).
tff(137,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)
| ~ totalorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z)
| ~ ssList(Z) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z)
| leq(V,X) ) )),
rewrite(( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z)
| leq(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ) )),
inference(bind,[status(th)],[]) ).
tff(138,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)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(V,X) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,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)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ) ),
inference(transitivity,[status(thm)],[138,136]) ).
tff(140,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)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(V,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause182) ).
tff(141,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ),
inference(modus_ponens,[status(thm)],[141,130]) ).
tff(143,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) ),
inference(modus_ponens,[status(thm)],[143,129]) ).
tff(145,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) )
| ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| leq(sk6,sk7)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))) )
<=> ( ~ ! [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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) )
| ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| leq(sk6,sk7)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
( ( ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssList(sk9)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| leq(sk6,sk7) )
<=> ( ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| leq(sk6,sk7)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) )
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssList(sk9)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| leq(sk6,sk7) )
<=> ( ~ ! [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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) )
| ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| leq(sk6,sk7)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))) ) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) )
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssList(sk9)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| leq(sk6,sk7) )
<=> ( ~ ! [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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) )
| ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| leq(sk6,sk7)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))) ) ),
inference(transitivity,[status(thm)],[147,145]) ).
tff(149,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) )
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssList(sk9)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| leq(sk6,sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,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)))
| ~ totalorderedP(app(app(U,cons(V,W)),cons(X,Y)))
| leq(V,X) )
| ~ ssList(sk10)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| leq(sk6,sk7)
| ~ ssList(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10)))
| ~ totalorderedP(app(app(sk8,cons(sk6,sk9)),cons(sk7,sk10))) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
leq(sk6,sk7),
inference(unit_resolution,[status(thm)],[150,144,10,60,30,50,67,127,120]) ).
tff(152,plain,
( lt(sk7,sk6)
<=> lt(sk7,sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,axiom,
lt(sk7,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(154,plain,
lt(sk7,sk6),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(156,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ lt(U,V)
| ~ lt(V,U) ) )),
( ( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssItem(U)
| ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) )),
( ( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(159,plain,
( ! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) ),
inference(quant_intro,[status(thm)],[158]) ).
tff(160,axiom,
! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause114) ).
tff(161,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ),
inference(modus_ponens,[status(thm)],[161,157]) ).
tff(163,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ),
inference(skolemize,[status(sab)],[162]) ).
tff(164,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ),
inference(modus_ponens,[status(thm)],[163,156]) ).
tff(165,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ lt(sk6,sk7)
| ~ lt(sk7,sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ lt(sk6,sk7)
| ~ lt(sk7,sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ lt(sk6,sk7)
| ~ lt(sk7,sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ~ lt(sk6,sk7)
| ~ lt(sk7,sk6) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
~ lt(sk6,sk7),
inference(unit_resolution,[status(thm)],[167,164,10,60,154]) ).
tff(169,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(170,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ leq(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| lt(U,V) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| ( U = V ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| ( U = V ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) )),
inference(bind,[status(th)],[]) ).
tff(173,plain,
( ! [V: $i,U: $i] :
( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| ( U = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,axiom,
! [V: $i,U: $i] :
( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause121) ).
tff(175,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ),
inference(modus_ponens,[status(thm)],[175,171]) ).
tff(177,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ),
inference(skolemize,[status(sab)],[176]) ).
tff(178,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ),
inference(modus_ponens,[status(thm)],[177,170]) ).
tff(179,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ( sk6 = sk7 )
| ~ leq(sk6,sk7) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ( sk6 = sk7 )
| ~ leq(sk6,sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,plain,
( ( ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ~ leq(sk6,sk7)
| ( sk6 = sk7 ) )
<=> ( ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ( sk6 = sk7 )
| ~ leq(sk6,sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ~ leq(sk6,sk7)
| ( sk6 = sk7 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ( sk6 = sk7 )
| ~ leq(sk6,sk7) ) ),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ~ leq(sk6,sk7)
| ( sk6 = sk7 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ( sk6 = sk7 )
| ~ leq(sk6,sk7) ) ),
inference(transitivity,[status(thm)],[181,179]) ).
tff(183,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ~ leq(sk6,sk7)
| ( sk6 = sk7 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| lt(sk6,sk7)
| ( sk6 = sk7 )
| ~ leq(sk6,sk7) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
( ( sk6 = sk7 )
| ~ leq(sk6,sk7) ),
inference(unit_resolution,[status(thm)],[184,178,10,60,168]) ).
tff(186,plain,
sk6 = sk7,
inference(unit_resolution,[status(thm)],[185,151]) ).
tff(187,plain,
sk7 = sk6,
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
( lt(sk7,sk7)
<=> lt(sk7,sk6) ),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
( lt(sk7,sk6)
<=> lt(sk7,sk7) ),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
lt(sk7,sk7),
inference(modus_ponens,[status(thm)],[154,189]) ).
tff(191,plain,
^ [V: $i] :
refl(( ( ~ ssItem(V)
| ~ lt(V,V) )
<=> ( ~ ssItem(V)
| ~ lt(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(192,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(quant_intro,[status(thm)],[191]) ).
tff(193,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(194,plain,
^ [V: $i] :
rewrite(( ( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ( ~ ssItem(V)
| ~ lt(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(195,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,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(197,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(198,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)],[197,196]) ).
tff(199,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)],[198,195]) ).
tff(200,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(201,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)],[200]) ).
tff(202,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)],[201,199]) ).
tff(203,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause111) ).
tff(204,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[204,193]) ).
tff(206,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(skolemize,[status(sab)],[205]) ).
tff(207,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[206,192]) ).
tff(208,plain,
( ( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk7)
| ~ lt(sk7,sk7) )
<=> ( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk7)
| ~ lt(sk7,sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk7)
| ~ lt(sk7,sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk7)
| ~ lt(sk7,sk7) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
~ lt(sk7,sk7),
inference(unit_resolution,[status(thm)],[210,207,60]) ).
tff(212,plain,
$false,
inference(unit_resolution,[status(thm)],[211,190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC303-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 08:54:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.30/1.46 % SZS status Unsatisfiable
% 1.30/1.46 % SZS output start Proof
% See solution above
% 1.30/1.49 % E exiting
%------------------------------------------------------------------------------