%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC161-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:30:21 AM UTC 2025
% Result : Unsatisfiable 1.37s 1.54s
% Output : Proof 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 83
% Syntax : Number of formulae : 190 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 1669 ( 162 equ)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 2755 (1364 ~;1265 |; 0 &)
% ( 126 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 88 ( 88 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 : 500 ( 456 !; 0 ?; 500 :)
% Comments :
%------------------------------------------------------------------------------
tff(strictorderedP_type,type,
strictorderedP: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk11_type,type,
sk11: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk10_type,type,
sk10: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk9_type,type,
sk9: $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(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = sk1 )
<=> ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(6,plain,
app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = sk1,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ssItem(sk7)
<=> ssItem(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
ssItem(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(9,plain,
ssItem(sk7),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(16,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(22,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(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(24,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(25,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)],[24,23]) ).
tff(26,plain,
ssList(cons(sk7,nil)),
inference(unit_resolution,[status(thm)],[25,22,19,9]) ).
tff(27,plain,
( ssList(sk9)
<=> ssList(sk9) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
ssList(sk9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(29,plain,
ssList(sk9),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(36,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ssList(app(sk9,cons(sk7,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ssList(app(sk9,cons(sk7,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil)))
| ~ ssList(sk9) )
<=> ( ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ssList(app(sk9,cons(sk7,nil))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil)))
| ~ ssList(sk9) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ssList(app(sk9,cons(sk7,nil))) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil)))
| ~ ssList(sk9) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ssList(app(sk9,cons(sk7,nil))) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil)))
| ~ ssList(sk9) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ssList(app(sk9,cons(sk7,nil))) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
ssList(app(sk9,cons(sk7,nil))),
inference(unit_resolution,[status(thm)],[45,39,29,26]) ).
tff(47,plain,
( ssList(sk10)
<=> ssList(sk10) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
ssList(sk10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(49,plain,
ssList(sk10),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ssList(sk10)
| ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ~ ssList(app(sk9,cons(sk7,nil))) )
<=> ( ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ~ ssList(app(sk9,cons(sk7,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ~ ssList(app(sk9,cons(sk7,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ~ ssList(app(sk9,cons(sk7,nil))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
ssList(app(app(sk9,cons(sk7,nil)),sk10)),
inference(unit_resolution,[status(thm)],[55,39,49,46]) ).
tff(57,plain,
( ssItem(sk8)
<=> ssItem(sk8) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
ssItem(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(59,plain,
ssItem(sk8),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk8)
| ~ ssList(nil)
| ssList(cons(sk8,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk8)
| ~ ssList(nil)
| ssList(cons(sk8,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk8)
| ~ ssList(nil)
| ssList(cons(sk8,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk8)
| ~ ssList(nil)
| ssList(cons(sk8,nil)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
ssList(cons(sk8,nil)),
inference(unit_resolution,[status(thm)],[62,22,19,59]) ).
tff(64,plain,
( ssList(sk11)
<=> ssList(sk11) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
ssList(sk11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(66,plain,
ssList(sk11),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,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(68,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)],[67]) ).
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(rewrite,[status(thm)],[]) ).
tff(70,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(71,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)],[70]) ).
tff(72,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(73,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)],[72,71]) ).
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)],[73,69]) ).
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(skolemize,[status(sab)],[74]) ).
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(modus_ponens,[status(thm)],[75,68]) ).
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)) ) )
| ~ ssList(sk11)
| ~ ssList(cons(sk8,nil))
| ~ ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk11)
| ~ ssList(cons(sk8,nil))
| ~ ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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(sk11)
| ~ ssList(cons(sk8,nil))
| ~ ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) ) ),
inference(quant_inst,[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(sk11)
| ~ ssList(cons(sk8,nil))
| ~ ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)),
inference(unit_resolution,[status(thm)],[79,76,66,63,56]) ).
tff(81,plain,
app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) = app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11),
inference(symmetry,[status(thm)],[80]) ).
tff(82,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(83,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)],[82]) ).
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(rewrite,[status(thm)],[]) ).
tff(85,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(86,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)],[85]) ).
tff(87,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(88,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk8)
| ~ ssList(sk11)
| ( app(cons(sk8,nil),sk11) = cons(sk8,sk11) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk8)
| ~ ssList(sk11)
| ( app(cons(sk8,nil),sk11) = cons(sk8,sk11) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk8)
| ~ ssList(sk11)
| ( app(cons(sk8,nil),sk11) = cons(sk8,sk11) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk8)
| ~ ssList(sk11)
| ( app(cons(sk8,nil),sk11) = cons(sk8,sk11) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
app(cons(sk8,nil),sk11) = cons(sk8,sk11),
inference(unit_resolution,[status(thm)],[94,91,59,66]) ).
tff(96,plain,
cons(sk8,sk11) = app(cons(sk8,nil),sk11),
inference(symmetry,[status(thm)],[95]) ).
tff(97,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(sk7,nil))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(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(cons(sk7,nil))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ( ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) )
<=> ( ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,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(sk9)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(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(cons(sk7,nil))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(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(cons(sk7,nil))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ) ),
inference(transitivity,[status(thm)],[99,97]) ).
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(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)),
inference(unit_resolution,[status(thm)],[102,76,29,49,26]) ).
tff(104,plain,
app(sk9,app(cons(sk7,nil),sk10)) = app(app(sk9,cons(sk7,nil)),sk10),
inference(symmetry,[status(thm)],[103]) ).
tff(105,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(106,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(107,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)],[106,105]) ).
tff(108,plain,
app(cons(sk7,nil),sk10) = cons(sk7,sk10),
inference(unit_resolution,[status(thm)],[107,91,9,49]) ).
tff(109,plain,
cons(sk7,sk10) = app(cons(sk7,nil),sk10),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
app(sk9,cons(sk7,sk10)) = app(sk9,app(cons(sk7,nil),sk10)),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
app(sk9,cons(sk7,sk10)) = app(app(sk9,cons(sk7,nil)),sk10),
inference(transitivity,[status(thm)],[110,104]) ).
tff(112,plain,
app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)),
inference(monotonicity,[status(thm)],[111,96]) ).
tff(113,plain,
app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) = sk3,
inference(transitivity,[status(thm)],[112,81,6,3]) ).
tff(114,plain,
( strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
<=> strictorderedP(sk3) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( strictorderedP(sk3)
<=> strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) ),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( strictorderedP(sk3)
<=> strictorderedP(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(118,plain,
strictorderedP(sk3),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))),
inference(modus_ponens,[status(thm)],[118,115]) ).
tff(120,plain,
( ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(121,plain,
( ssList(sk3)
<=> ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) ),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(124,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))),
inference(modus_ponens,[status(thm)],[124,121]) ).
tff(126,plain,
^ [V: $i] :
refl(( ( ~ ssItem(V)
| ~ lt(V,V) )
<=> ( ~ ssItem(V)
| ~ lt(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
^ [V: $i] :
rewrite(( ( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ( ~ ssItem(V)
| ~ lt(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [V: $i] :
( ~ ssItem(V)
| ~ ssItem(V)
| ~ lt(V,V) )
<=> ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,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(132,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(133,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)],[132,131]) ).
tff(134,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)],[133,130]) ).
tff(135,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(136,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)],[135]) ).
tff(137,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)],[136,134]) ).
tff(138,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(139,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[139,128]) ).
tff(141,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(skolemize,[status(sab)],[140]) ).
tff(142,plain,
! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) ),
inference(modus_ponens,[status(thm)],[141,127]) ).
tff(143,plain,
( ( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk8)
| ~ lt(sk8,sk8) )
<=> ( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk8)
| ~ lt(sk8,sk8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk8)
| ~ lt(sk8,sk8) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [V: $i] :
( ~ ssItem(V)
| ~ lt(V,V) )
| ~ ssItem(sk8)
| ~ lt(sk8,sk8) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
~ lt(sk8,sk8),
inference(unit_resolution,[status(thm)],[145,142,59]) ).
tff(147,plain,
( leq(sk8,sk7)
<=> leq(sk8,sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,axiom,
leq(sk8,sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
tff(149,plain,
leq(sk8,sk7),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,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(151,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)],[150]) ).
tff(152,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(153,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(154,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)],[153]) ).
tff(155,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/sandbox/benchmark/Axioms/SWC001-0.ax',clause147) ).
tff(156,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)],[155,154]) ).
tff(157,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)],[156,152]) ).
tff(158,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)],[157]) ).
tff(159,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)],[158,151]) ).
tff(160,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ leq(sk8,sk7)
| ~ lt(sk7,sk8) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ leq(sk8,sk7)
| ~ lt(sk7,sk8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,plain,
( ( ~ ssItem(sk8)
| ~ ssItem(sk7)
| ~ leq(sk8,sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ lt(sk7,sk8) )
<=> ( ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ leq(sk8,sk7)
| ~ lt(sk7,sk8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk8)
| ~ ssItem(sk7)
| ~ leq(sk8,sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ lt(sk7,sk8) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ leq(sk8,sk7)
| ~ lt(sk7,sk8) ) ),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk8)
| ~ ssItem(sk7)
| ~ leq(sk8,sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ lt(sk7,sk8) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ leq(sk8,sk7)
| ~ lt(sk7,sk8) ) ),
inference(transitivity,[status(thm)],[162,160]) ).
tff(164,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk8)
| ~ ssItem(sk7)
| ~ leq(sk8,sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ lt(sk7,sk8) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(W)
| lt(U,W)
| ~ lt(V,W) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk8,sk8)
| ~ leq(sk8,sk7)
| ~ lt(sk7,sk8) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
~ lt(sk7,sk8),
inference(unit_resolution,[status(thm)],[165,159,9,59,149,146]) ).
tff(167,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(168,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)],[167]) ).
tff(169,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(170,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(171,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)],[170]) ).
tff(172,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(173,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(174,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)],[173,172]) ).
tff(175,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)],[174,171]) ).
tff(176,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(177,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)],[176]) ).
tff(178,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)],[177,175]) ).
tff(179,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/sandbox/benchmark/Axioms/SWC001-0.ax',clause181) ).
tff(180,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)],[179,178]) ).
tff(181,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)],[180,169]) ).
tff(182,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)],[181]) ).
tff(183,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)],[182,168]) ).
tff(184,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))) )
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk10)
| lt(sk7,sk8)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) )
<=> ( ~ ! [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))) )
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk10)
| lt(sk7,sk8)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,plain,
( ( ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| lt(sk7,sk8)
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) )
<=> ( ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk10)
| lt(sk7,sk8)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,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(sk8)
| ~ ssList(sk9)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| lt(sk7,sk8)
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) )
<=> ( ~ ! [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))) )
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk10)
| lt(sk7,sk8)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) ) ),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,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(sk8)
| ~ ssList(sk9)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| lt(sk7,sk8)
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) )
<=> ( ~ ! [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))) )
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk10)
| lt(sk7,sk8)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) ) ),
inference(transitivity,[status(thm)],[186,184]) ).
tff(188,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(sk8)
| ~ ssList(sk9)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| lt(sk7,sk8)
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,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))) )
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk10)
| lt(sk7,sk8)
| ~ ssList(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)))
| ~ strictorderedP(app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11))) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
$false,
inference(unit_resolution,[status(thm)],[189,183,9,59,29,49,66,166,125,119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC161-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:27:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.37/1.54 % SZS status Unsatisfiable
% 1.37/1.54 % SZS output start Proof
% See solution above
% 1.41/1.57 % E exiting
%------------------------------------------------------------------------------