%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC042-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:00 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 44 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 215 ( 110 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 305 ( 148 ~; 133 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(nil_type,type,
nil: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ( nil = sk2 )
<=> ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
nil = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk2 = nil,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(7,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ( app(sk3,sk5) = sk4 )
<=> ( app(sk3,sk5) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(11,plain,
app(sk3,sk5) = sk4,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
app(sk3,sk5) = nil,
inference(transitivity,[status(thm)],[11,8,4]) ).
tff(13,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(15,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(20,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(24,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(27,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
tff(34,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ( nil = sk3 )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ( app(sk3,sk5) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ( nil = sk3 )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ( app(sk3,sk5) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ~ ssList(sk5)
| ( app(sk3,sk5) != nil ) )
<=> ( ( nil = sk3 )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ( app(sk3,sk5) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ ssList(sk5)
| ( app(sk3,sk5) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ( nil = sk3 )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ( app(sk3,sk5) != nil ) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ ssList(sk5)
| ( app(sk3,sk5) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ( nil = sk3 )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ( app(sk3,sk5) != nil ) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ ssList(sk5)
| ( app(sk3,sk5) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ( nil = sk3 )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ( app(sk3,sk5) != nil ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,37,27,24,21,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC042-1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 08:07:31 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% See solution above
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------