TSTP Solution File: SWC394-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC394-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Tue Sep 20 11:57:39 EDT 2022
% Result : Unsatisfiable 38.85s 25.20s
% Output : Proof 38.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 144
% Syntax : Number of formulae : 335 ( 99 unt; 16 typ; 0 def)
% Number of atoms : 2106 ( 323 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 3302 (1609 ~;1517 |; 0 &)
% ( 176 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 94 ( 94 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 673 ( 625 !; 0 ?; 673 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssList_type,type,
ssList: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf42_type,type,
skaf42: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf47_type,type,
skaf47: ( $i * $i ) > $i ).
tff(sk4_type,type,
sk4: $i ).
tff(nil_type,type,
nil: $i ).
tff(skaf48_type,type,
skaf48: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(skaf43_type,type,
skaf43: ( $i * $i ) > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf47(U,V))
<=> ssList(skaf47(U,V)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ssList(skaf47(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf47(U,V)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ssList(skaf47(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf47(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause49) ).
tff(5,plain,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ssList(skaf47(U,V)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf47(U,V))
| ssList(skaf47(sk3,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ssList(skaf47(sk3,sk3)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,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)],[13]) ).
tff(15,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(16,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(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] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ssList(app(skaf47(sk3,sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ssList(app(skaf47(sk3,sk3),nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ ssList(nil)
| ssList(app(skaf47(sk3,sk3),nil))
| ~ ssList(skaf47(sk3,sk3)) )
<=> ( ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ssList(app(skaf47(sk3,sk3),nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ssList(app(skaf47(sk3,sk3),nil))
| ~ ssList(skaf47(sk3,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ssList(app(skaf47(sk3,sk3),nil)) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ssList(app(skaf47(sk3,sk3),nil))
| ~ ssList(skaf47(sk3,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ssList(app(skaf47(sk3,sk3),nil)) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ssList(app(skaf47(sk3,sk3),nil))
| ~ ssList(skaf47(sk3,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ssList(app(skaf47(sk3,sk3),nil)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
ssList(app(skaf47(sk3,sk3),nil)),
inference(unit_resolution,[status(thm)],[28,22,19,9]) ).
tff(30,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf48(U,V))
<=> ssList(skaf48(U,V)) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [V: $i,U: $i] : ssList(skaf48(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf48(U,V)) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [V: $i,U: $i] : ssList(skaf48(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf48(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause48) ).
tff(34,plain,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V: $i,U: $i] : ssList(skaf48(U,V)),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf48(U,V))
| ssList(skaf48(sk3,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
ssList(skaf48(sk3,sk3)),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(42,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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(48,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)],[47]) ).
tff(49,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(50,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)],[49,48]) ).
tff(51,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)],[50,46]) ).
tff(52,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)],[51]) ).
tff(53,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)],[52,45]) ).
tff(54,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf48(sk3,sk3))
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf48(sk3,sk3))
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ ssList(skaf48(sk3,sk3))
| ~ ssList(sk3)
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) )
<=> ( ~ ssList(sk3)
| ~ ssList(skaf48(sk3,sk3))
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf48(sk3,sk3))
| ~ ssList(sk3)
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf48(sk3,sk3))
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf48(sk3,sk3))
| ~ ssList(sk3)
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf48(sk3,sk3))
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf48(sk3,sk3))
| ~ ssList(sk3)
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf48(sk3,sk3))
| ~ ssList(app(skaf47(sk3,sk3),nil))
| ( app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))),
inference(unit_resolution,[status(thm)],[59,53,43,38,29]) ).
tff(61,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(65,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[70,67,43]) ).
tff(72,plain,
app(skaf47(sk3,sk3),app(nil,sk3)) = app(skaf47(sk3,sk3),sk3),
inference(monotonicity,[status(thm)],[71]) ).
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)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
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)) ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) ) ),
inference(monotonicity,[status(thm)],[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)) ) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
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(sk3)
| ~ ssList(nil)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) ),
inference(quant_inst,[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(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ ssList(skaf47(sk3,sk3))
| ( app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)) ) ),
inference(unit_resolution,[status(thm)],[78,22,53,43]) ).
tff(80,plain,
app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),app(nil,sk3)),
inference(unit_resolution,[status(thm)],[79,9]) ).
tff(81,plain,
app(app(skaf47(sk3,sk3),nil),sk3) = app(skaf47(sk3,sk3),sk3),
inference(transitivity,[status(thm)],[80,72]) ).
tff(82,plain,
app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)) = app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = app(app(app(skaf47(sk3,sk3),nil),sk3),skaf48(sk3,sk3)),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(88,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
segmentP(sk3,sk3),
inference(unit_resolution,[status(thm)],[93,90,43]) ).
tff(95,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ segmentP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,axiom,
! [V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause168) ).
tff(101,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ),
inference(modus_ponens,[status(thm)],[103,96]) ).
tff(105,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) )
<=> ( ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) ) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) ) ),
inference(transitivity,[status(thm)],[107,105]) ).
tff(109,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| ( app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)) = sk3,
inference(unit_resolution,[status(thm)],[110,104,43,94]) ).
tff(112,plain,
sk3 = app(app(skaf47(sk3,sk3),sk3),skaf48(sk3,sk3)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
sk3 = app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))),
inference(transitivity,[status(thm)],[112,83,60]) ).
tff(114,plain,
app(skaf47(sk4,sk3),sk3) = app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf47(U,V))
| ssList(skaf47(sk4,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
ssList(skaf47(sk4,sk3)),
inference(unit_resolution,[status(thm)],[115,7]) ).
tff(117,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(skaf47(sk4,sk3))
| ( app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3) ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(skaf47(sk4,sk3))
| ( app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(skaf47(sk4,sk3))
| ( app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(skaf47(sk4,sk3))
| ( app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3) ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
app(nil,skaf47(sk4,sk3)) = skaf47(sk4,sk3),
inference(unit_resolution,[status(thm)],[119,67,116]) ).
tff(121,plain,
app(app(nil,skaf47(sk4,sk3)),sk3) = app(skaf47(sk4,sk3),sk3),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ( ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(nil)
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(nil)
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ) ),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(nil)
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ) ),
inference(transitivity,[status(thm)],[124,122]) ).
tff(126,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ~ ssList(nil)
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
app(app(nil,skaf47(sk4,sk3)),sk3) = app(nil,app(skaf47(sk4,sk3),sk3)),
inference(unit_resolution,[status(thm)],[127,22,53,43,116]) ).
tff(129,plain,
app(nil,app(skaf47(sk4,sk3),sk3)) = app(app(nil,skaf47(sk4,sk3)),sk3),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
( memberP(sk1,sk5)
<=> memberP(sk3,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( memberP(sk1,sk5)
<=> memberP(sk1,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(132,axiom,
memberP(sk1,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(133,plain,
memberP(sk1,sk5),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
memberP(sk3,sk5),
inference(modus_ponens,[status(thm)],[133,130]) ).
tff(135,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(136,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(137,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(139,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(142,plain,
( ! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,axiom,
! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
tff(144,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[144,140]) ).
tff(146,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(skolemize,[status(sab)],[145]) ).
tff(147,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[146,139]) ).
tff(148,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ memberP(sk3,sk5)
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3 ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = sk3,
inference(unit_resolution,[status(thm)],[150,147,43,137,134]) ).
tff(152,plain,
app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) = app(skaf47(sk4,sk3),sk3),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf42(U,V))
<=> ssList(skaf42(U,V)) )),
inference(bind,[status(th)],]) ).
tff(154,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(quant_intro,[status(thm)],[153]) ).
tff(155,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(156,axiom,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
tff(157,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(skolemize,[status(sab)],[157]) ).
tff(159,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[158,154]) ).
tff(160,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf42(U,V))
| ssList(skaf42(sk3,sk5)) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
ssList(skaf42(sk3,sk5)),
inference(unit_resolution,[status(thm)],[160,159]) ).
tff(162,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf43(U,V))
<=> ssList(skaf43(U,V)) )),
inference(bind,[status(th)],]) ).
tff(163,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(165,axiom,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
tff(166,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf43(U,V))
| ssList(skaf43(sk5,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
ssList(skaf43(sk5,sk3)),
inference(unit_resolution,[status(thm)],[169,168]) ).
tff(171,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(172,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)],[171]) ).
tff(173,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(174,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(175,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)],[174]) ).
tff(176,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(177,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[177,173]) ).
tff(179,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[178]) ).
tff(180,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[179,172]) ).
tff(181,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(182,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
( ~ ssList(skaf43(sk5,sk3))
| ssList(cons(sk5,skaf43(sk5,sk3))) ),
inference(unit_resolution,[status(thm)],[183,180,137]) ).
tff(185,plain,
ssList(cons(sk5,skaf43(sk5,sk3))),
inference(unit_resolution,[status(thm)],[184,170]) ).
tff(186,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
( ~ ssList(skaf47(sk4,sk3))
| ( app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(unit_resolution,[status(thm)],[188,53,185,161]) ).
tff(190,plain,
app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3)))),
inference(unit_resolution,[status(thm)],[189,116]) ).
tff(191,plain,
app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),sk3),
inference(transitivity,[status(thm)],[190,152]) ).
tff(192,plain,
app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) = app(nil,app(skaf47(sk4,sk3),sk3)),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
( ( ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ) ),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ) ),
inference(transitivity,[status(thm)],[195,193]) ).
tff(197,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(skaf47(sk4,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(skaf42(sk3,sk5))
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5))),
inference(unit_resolution,[status(thm)],[198,19,161,116]) ).
tff(200,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,plain,
( ( ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(nil)
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(nil)
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(nil)
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ) ),
inference(transitivity,[status(thm)],[202,200]) ).
tff(204,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ~ ssList(nil)
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(cons(sk5,skaf43(sk5,sk3)))
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))) ) ),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(nil,app(app(skaf47(sk4,sk3),skaf42(sk3,sk5)),cons(sk5,skaf43(sk5,sk3)))),
inference(unit_resolution,[status(thm)],[205,22,53,185,199]) ).
tff(207,plain,
app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) = app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),
inference(transitivity,[status(thm)],[206,192,129,121,114]) ).
tff(208,plain,
app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) = app(skaf47(sk4,sk3),sk3),
inference(symmetry,[status(thm)],[114]) ).
tff(209,plain,
( memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
<=> memberP(app(skaf47(sk4,sk3),sk3),sk5) ),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
( memberP(app(skaf47(sk4,sk3),sk3),sk5)
<=> memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5) ),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
<=> ~ memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5) ),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
( ( ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(214,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ) ),
inference(transitivity,[status(thm)],[214,212]) ).
tff(216,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssList(skaf47(sk4,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(217,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
( ~ ssList(skaf47(sk4,sk3))
| ssList(app(skaf47(sk4,sk3),sk3)) ),
inference(unit_resolution,[status(thm)],[217,19,43]) ).
tff(219,plain,
ssList(app(skaf47(sk4,sk3),sk3)),
inference(unit_resolution,[status(thm)],[218,116]) ).
tff(220,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],]) ).
tff(221,plain,
( ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(222,plain,
( ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[221,220]) ).
tff(223,plain,
( ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(225,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[224]) ).
tff(226,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(227,plain,
^ [U: $i] :
rewrite(
( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(228,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[227]) ).
tff(229,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(230,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[229,228]) ).
tff(231,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[230,226]) ).
tff(232,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[231]) ).
tff(233,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[232,225]) ).
tff(234,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(235,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(236,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(modus_ponens,[status(thm)],[235,234]) ).
tff(237,plain,
~ memberP(nil,sk5),
inference(unit_resolution,[status(thm)],[236,233,137]) ).
tff(238,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(239,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[238]) ).
tff(240,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(241,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(242,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[241]) ).
tff(243,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause175) ).
tff(244,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[244,240]) ).
tff(246,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(skolemize,[status(sab)],[245]) ).
tff(247,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ),
inference(modus_ponens,[status(thm)],[246,239]) ).
tff(248,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(249,plain,
( ( ~ ssList(nil)
| ~ ssList(skaf42(sk3,sk5))
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(250,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(skaf42(sk3,sk5))
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ) ),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(skaf42(sk3,sk5))
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ) ),
inference(transitivity,[status(thm)],[250,248]) ).
tff(252,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssList(skaf42(sk3,sk5))
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(253,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(nil,sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ),
inference(modus_ponens,[status(thm)],[252,251]) ).
tff(254,plain,
( ~ ssList(skaf43(sk5,sk3))
| ~ ssList(skaf42(sk3,sk5))
| ( app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil ) ),
inference(unit_resolution,[status(thm)],[253,22,247,137,237]) ).
tff(255,plain,
app(skaf42(sk3,sk5),cons(sk5,skaf43(sk5,sk3))) != nil,
inference(unit_resolution,[status(thm)],[254,170,161]) ).
tff(256,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[255,223]) ).
tff(257,plain,
( ( ( nil = sk3 )
| segmentP(sk4,sk3) )
<=> ( ( nil = sk3 )
| segmentP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(258,axiom,
( ( nil = sk3 )
| segmentP(sk4,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(259,plain,
( ( nil = sk3 )
| segmentP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[258,257]) ).
tff(260,plain,
segmentP(sk4,sk3),
inference(unit_resolution,[status(thm)],[259,256]) ).
tff(261,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(262,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(263,axiom,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
tff(264,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[263,262]) ).
tff(265,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[264,261]) ).
tff(266,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(267,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(268,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ) ),
inference(transitivity,[status(thm)],[268,266]) ).
tff(270,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(271,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ( app(app(skaf47(U,V),V),skaf48(V,U)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(sk4,sk3)
| ( app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)) = sk4,
inference(unit_resolution,[status(thm)],[271,104,43,265,260]) ).
tff(273,plain,
( memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5)
<=> memberP(sk4,sk5) ),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
( memberP(sk4,sk5)
<=> memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
( ~ memberP(sk4,sk5)
<=> ~ memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
( ~ memberP(sk2,sk5)
<=> ~ memberP(sk4,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(277,plain,
( ~ memberP(sk2,sk5)
<=> ~ memberP(sk2,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(278,axiom,
~ memberP(sk2,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(279,plain,
~ memberP(sk2,sk5),
inference(modus_ponens,[status(thm)],[278,277]) ).
tff(280,plain,
~ memberP(sk4,sk5),
inference(modus_ponens,[status(thm)],[279,276]) ).
tff(281,plain,
~ memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5),
inference(modus_ponens,[status(thm)],[280,275]) ).
tff(282,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf48(U,V))
| ssList(skaf48(sk3,sk4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(283,plain,
ssList(skaf48(sk3,sk4)),
inference(unit_resolution,[status(thm)],[282,36]) ).
tff(284,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
inference(bind,[status(th)],]) ).
tff(285,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(quant_intro,[status(thm)],[284]) ).
tff(286,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(287,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(U,V)
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) )),
inference(bind,[status(th)],]) ).
tff(288,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ) ),
inference(quant_intro,[status(thm)],[287]) ).
tff(289,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause140) ).
tff(290,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[289,288]) ).
tff(291,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[290,286]) ).
tff(292,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(skolemize,[status(sab)],[291]) ).
tff(293,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) ),
inference(modus_ponens,[status(thm)],[292,285]) ).
tff(294,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(295,plain,
( ( ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(296,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(monotonicity,[status(thm)],[295]) ).
tff(297,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ) ),
inference(transitivity,[status(thm)],[296,294]) ).
tff(298,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(299,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssItem(sk5)
| ~ ssList(skaf48(sk3,sk4))
| ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(modus_ponens,[status(thm)],[298,297]) ).
tff(300,plain,
( ~ ssList(app(skaf47(sk4,sk3),sk3))
| ~ memberP(app(skaf47(sk4,sk3),sk3),sk5)
| memberP(app(app(skaf47(sk4,sk3),sk3),skaf48(sk3,sk4)),sk5) ),
inference(unit_resolution,[status(thm)],[299,293,137,283]) ).
tff(301,plain,
~ memberP(app(skaf47(sk4,sk3),sk3),sk5),
inference(unit_resolution,[status(thm)],[300,281,219]) ).
tff(302,plain,
~ memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5),
inference(modus_ponens,[status(thm)],[301,211]) ).
tff(303,plain,
( ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
<=> ssList(app(skaf47(sk4,sk3),sk3)) ),
inference(monotonicity,[status(thm)],[208]) ).
tff(304,plain,
( ssList(app(skaf47(sk4,sk3),sk3))
<=> ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))))) ),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3))))),
inference(modus_ponens,[status(thm)],[219,304]) ).
tff(306,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(307,plain,
( ( ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssItem(sk5)
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) )
<=> ( ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(308,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssItem(sk5)
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) ) ),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssItem(sk5)
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) ) ),
inference(transitivity,[status(thm)],[308,306]) ).
tff(310,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssItem(sk5)
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(skaf43(sk5,sk3))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(311,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk3))
| ~ ssList(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))))
| memberP(app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))),sk5)
| ~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ( app(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))),cons(sk5,skaf43(sk5,sk3))) != app(skaf47(sk4,sk3),app(app(skaf47(sk3,sk3),nil),app(sk3,skaf48(sk3,sk3)))) ) ),
inference(modus_ponens,[status(thm)],[310,309]) ).
tff(312,plain,
~ ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))),
inference(unit_resolution,[status(thm)],[311,247,137,170,305,302,207]) ).
tff(313,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(314,plain,
( ( ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssList(nil) )
<=> ( ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(315,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ) ),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssList(nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ) ),
inference(transitivity,[status(thm)],[315,313]) ).
tff(317,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5))))
| ~ ssList(nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(318,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(nil)
| ~ ssList(app(skaf47(sk4,sk3),skaf42(sk3,sk5)))
| ssList(app(nil,app(skaf47(sk4,sk3),skaf42(sk3,sk5)))) ),
inference(modus_ponens,[status(thm)],[317,316]) ).
tff(319,plain,
$false,
inference(unit_resolution,[status(thm)],[318,22,19,199,312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SWC394-1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 00:34:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 38.85/25.20 % SZS status Unsatisfiable
% 38.85/25.20 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------