%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC398-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:07 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 49 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 242 ( 15 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 339 ( 166 ~; 145 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk6_type,type,
sk6: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( memberP(sk3,sk6)
<=> memberP(sk1,sk6) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( memberP(sk1,sk6)
<=> memberP(sk3,sk6) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( memberP(sk1,sk6)
<=> memberP(sk1,sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
memberP(sk1,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(9,plain,
memberP(sk1,sk6),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
memberP(sk3,sk6),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(13,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ( app(sk3,sk5) = sk4 )
<=> ( app(sk3,sk5) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(17,plain,
app(sk3,sk5) = sk4,
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(sk3,sk5) = sk2,
inference(transitivity,[status(thm)],[17,14]) ).
tff(19,plain,
( memberP(app(sk3,sk5),sk6)
<=> memberP(sk2,sk6) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( memberP(sk2,sk6)
<=> memberP(app(sk3,sk5),sk6) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ~ memberP(sk2,sk6)
<=> ~ memberP(app(sk3,sk5),sk6) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ~ memberP(sk2,sk6)
<=> ~ memberP(sk2,sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
~ memberP(sk2,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(24,plain,
~ memberP(sk2,sk6),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ memberP(app(sk3,sk5),sk6),
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(28,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(31,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(34,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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(39,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)],[38]) ).
tff(40,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(41,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)],[40,39]) ).
tff(42,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)],[41,37]) ).
tff(43,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)],[42]) ).
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)],[43,36]) ).
tff(45,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(sk3)
| ~ ssItem(sk6)
| ~ ssList(sk5)
| ~ memberP(sk3,sk6)
| memberP(app(sk3,sk5),sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(sk3)
| ~ ssItem(sk6)
| ~ ssList(sk5)
| ~ memberP(sk3,sk6)
| memberP(app(sk3,sk5),sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(sk3)
| ~ ssItem(sk6)
| ~ ssList(sk5)
| ~ memberP(sk3,sk6)
| memberP(app(sk3,sk5),sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ memberP(U,V)
| memberP(app(U,W),V) )
| ~ ssList(sk3)
| ~ ssItem(sk6)
| ~ ssList(sk5)
| ~ memberP(sk3,sk6)
| memberP(app(sk3,sk5),sk6) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ~ memberP(sk3,sk6)
| memberP(app(sk3,sk5),sk6) ),
inference(unit_resolution,[status(thm)],[47,44,34,31,28]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,25,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC398-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:14:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------