TSTP Solution File: SWC399-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC399-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 11:57:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 46
% Syntax : Number of formulae : 86 ( 24 unt; 10 typ; 0 def)
% Number of atoms : 623 ( 0 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 993 ( 488 ~; 451 |; 0 &)
% ( 54 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 168 ( 152 !; 0 ?; 168 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk7_type,type,
sk7: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(3,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(7,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,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(10,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)],[9]) ).
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(rewrite,[status(thm)],]) ).
tff(12,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(13,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)],[12]) ).
tff(14,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(15,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ssList(app(sk5,sk3)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ssList(app(sk5,sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( ~ ssList(sk3)
| ssList(app(sk5,sk3))
| ~ ssList(sk5) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk5)
| ssList(app(sk5,sk3)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(sk5,sk3))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ssList(app(sk5,sk3)) ) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(sk5,sk3))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ssList(app(sk5,sk3)) ) ),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ssList(app(sk5,sk3))
| ~ ssList(sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ssList(app(sk5,sk3)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
ssList(app(sk5,sk3)),
inference(unit_resolution,[status(thm)],[24,18,8,3]) ).
tff(26,plain,
( ~ memberP(sk2,sk7)
<=> ~ memberP(app(app(sk5,sk3),sk6),sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ memberP(sk2,sk7)
<=> ~ memberP(sk2,sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
~ memberP(sk2,sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(29,plain,
~ memberP(sk2,sk7),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
~ memberP(app(app(sk5,sk3),sk6),sk7),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,plain,
( ssItem(sk7)
<=> ssItem(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
ssItem(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(33,plain,
ssItem(sk7),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(36,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,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(38,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)],[37]) ).
tff(39,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(40,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(41,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)],[40]) ).
tff(42,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
tff(43,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)],[42,41]) ).
tff(44,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)],[43,39]) ).
tff(45,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)],[44]) ).
tff(46,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)],[45,38]) ).
tff(47,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(app(sk5,sk3),sk6),sk7)
| ~ ssList(sk6)
| ~ ssItem(sk7)
| ~ ssList(app(sk5,sk3))
| ~ memberP(app(sk5,sk3),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(app(sk5,sk3),sk6),sk7)
| ~ ssList(sk6)
| ~ ssItem(sk7)
| ~ ssList(app(sk5,sk3))
| ~ memberP(app(sk5,sk3),sk7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( ~ ssList(app(sk5,sk3))
| ~ ssItem(sk7)
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk3),sk7)
| memberP(app(app(sk5,sk3),sk6),sk7) )
<=> ( memberP(app(app(sk5,sk3),sk6),sk7)
| ~ ssList(sk6)
| ~ ssItem(sk7)
| ~ ssList(app(sk5,sk3))
| ~ memberP(app(sk5,sk3),sk7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(sk5,sk3))
| ~ ssItem(sk7)
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk3),sk7)
| memberP(app(app(sk5,sk3),sk6),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(app(sk5,sk3),sk6),sk7)
| ~ ssList(sk6)
| ~ ssItem(sk7)
| ~ ssList(app(sk5,sk3))
| ~ memberP(app(sk5,sk3),sk7) ) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(sk5,sk3))
| ~ ssItem(sk7)
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk3),sk7)
| memberP(app(app(sk5,sk3),sk6),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(app(sk5,sk3),sk6),sk7)
| ~ ssList(sk6)
| ~ ssItem(sk7)
| ~ ssList(app(sk5,sk3))
| ~ memberP(app(sk5,sk3),sk7) ) ),
inference(transitivity,[status(thm)],[49,47]) ).
tff(51,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(app(sk5,sk3))
| ~ ssItem(sk7)
| ~ ssList(sk6)
| ~ memberP(app(sk5,sk3),sk7)
| memberP(app(app(sk5,sk3),sk6),sk7) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| memberP(app(app(sk5,sk3),sk6),sk7)
| ~ ssList(sk6)
| ~ ssItem(sk7)
| ~ ssList(app(sk5,sk3))
| ~ memberP(app(sk5,sk3),sk7) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ~ ssList(app(sk5,sk3))
| ~ memberP(app(sk5,sk3),sk7) ),
inference(unit_resolution,[status(thm)],[52,46,36,33,30]) ).
tff(54,plain,
~ memberP(app(sk5,sk3),sk7),
inference(unit_resolution,[status(thm)],[53,25]) ).
tff(55,plain,
( memberP(sk1,sk7)
<=> memberP(sk3,sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( memberP(sk1,sk7)
<=> memberP(sk1,sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
memberP(sk1,sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(58,plain,
memberP(sk1,sk7),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
memberP(sk3,sk7),
inference(modus_ponens,[status(thm)],[58,55]) ).
tff(60,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ memberP(U,V)
| ~ ssList(W) ) )),
rewrite(
( ( ~ ssList(U)
| ~ memberP(U,V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ 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(U)
| ~ ssList(W)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
( ( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [W: $i,V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
tff(66,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk7)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk7)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ ssList(sk3)
| ~ ssItem(sk7)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk7)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssItem(sk7)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk7)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssItem(sk7)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk7)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssItem(sk7)
| ~ ssList(sk5)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(W,U),V) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssItem(sk7)
| ~ memberP(sk3,sk7)
| memberP(app(sk5,sk3),sk7) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
$false,
inference(unit_resolution,[status(thm)],[75,69,8,3,33,59,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC399-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 00:40:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.48 % SZS status Unsatisfiable
% 0.19/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------