%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC255+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:30:42 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 550 ( 86 equ)
% Maximal formula atoms : 12 ( 61 avg)
% Number of connectives : 772 ( 313 ~; 308 |; 45 &)
% ( 46 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 82 ( 82 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 64 ( 60 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(singletonP_type,type,
singletonP: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ! [U: $i] : $true
<=> $true ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(3,plain,
^ [U: $i] :
trans(monotonicity(trans(quant_intro(proof_bind(^ [V: $i] :
trans(monotonicity(trans(quant_intro(proof_bind(^ [W: $i] :
trans(monotonicity(trans(quant_intro(proof_bind(^ [X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) )
<=> ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) )),
( ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) )
<=> ( ( V != X )
| ( U != W )
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )),
rewrite(( ( ( V != X )
| ( U != W )
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) )
<=> ( ( U != W )
| ( V != X )
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )),
( ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) )
<=> ( ( U != W )
| ( V != X )
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )),
( ( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )
<=> ( ssList(X)
=> ( ( U != W )
| ( V != X )
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) )),
rewrite(( ( ssList(X)
=> ( ( U != W )
| ( V != X )
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )
<=> ( ( U != W )
| ( V != X )
| ~ ssList(X)
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )),
( ( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )
<=> ( ( U != W )
| ( V != X )
| ~ ssList(X)
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ))),
( ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )
<=> ! [X: $i] :
( ( U != W )
| ( V != X )
| ~ ssList(X)
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )),
trans(trans(der(( ! [X: $i] :
( ( U != W )
| ( V != X )
| ~ ssList(X)
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) )
<=> ! [X: $i] :
( ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(V,nil) ) )
| ( U != W )
| ~ ssList(V) ) )),
elim_unused(( ! [X: $i] :
( ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(V,nil) ) )
| ( U != W )
| ~ ssList(V) )
<=> ( ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(V,nil) ) )
| ( U != W )
| ~ ssList(V) ) )),
( ! [X: $i] :
( ( U != W )
| ( V != X )
| ~ ssList(X)
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) )
<=> ( ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(V,nil) ) )
| ( U != W )
| ~ ssList(V) ) )),
trans(monotonicity(trans(monotonicity(rewrite(( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
<=> ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) ) )),
rewrite(( ( ~ neq(V,nil)
| neq(V,nil) )
<=> $true )),
( ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(V,nil) ) )
<=> ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& $true ) )),
rewrite(( ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& $true )
<=> ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) ) )),
( ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(V,nil) ) )
<=> ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) ) )),
( ( ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(V,nil) ) )
| ( U != W )
| ~ ssList(V) )
<=> ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ( U != W )
| ~ ssList(V) ) )),
rewrite(( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ( U != W )
| ~ ssList(V) )
<=> ( ( U != W )
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) ) )),
( ( ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(V,nil) ) )
| ( U != W )
| ~ ssList(V) )
<=> ( ( U != W )
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) ) )),
( ! [X: $i] :
( ( U != W )
| ( V != X )
| ~ ssList(X)
| ( ( singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) )
<=> ( ( U != W )
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) ) )),
( ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) )
<=> ( ( U != W )
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) ) )),
( ( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) )
<=> ( ssList(W)
=> ( ( U != W )
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) ) ) )),
rewrite(( ( ssList(W)
=> ( ( U != W )
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) ) )
<=> ( ( U != W )
| ~ ssList(W)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) ) )),
( ( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) )
<=> ( ( U != W )
| ~ ssList(W)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) ) ))),
( ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) )
<=> ! [W: $i] :
( ( U != W )
| ~ ssList(W)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) ) )),
trans(trans(der(( ! [W: $i] :
( ( U != W )
| ~ ssList(W)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) )
<=> ! [W: $i] :
( ~ ssList(V)
| ~ ssList(U)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(U) ) )),
elim_unused(( ! [W: $i] :
( ~ ssList(V)
| ~ ssList(U)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(U) )
<=> ( ~ ssList(V)
| ~ ssList(U)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(U) ) )),
( ! [W: $i] :
( ( U != W )
| ~ ssList(W)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ ssList(U)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(U) ) )),
rewrite(( ( ~ ssList(V)
| ~ ssList(U)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(U) )
<=> $true )),
( ! [W: $i] :
( ( U != W )
| ~ ssList(W)
| singletonP(U)
| ~ neq(V,nil)
| ~ singletonP(W)
| ~ ssList(V) )
<=> $true )),
( ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) )
<=> $true )),
( ( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) )
<=> ( ssList(V)
=> $true ) )),
rewrite(( ( ssList(V)
=> $true )
<=> $true )),
( ( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) )
<=> $true ))),
( ! [V: $i] :
( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) )
<=> ! [V: $i] : $true )),
elim_unused(( ! [V: $i] : $true
<=> $true )),
( ! [V: $i] :
( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) )
<=> $true )),
( ( ssList(U)
=> ! [V: $i] :
( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) )
<=> ( ssList(U)
=> $true ) )),
rewrite(( ( ssList(U)
=> $true )
<=> $true )),
( ( ssList(U)
=> ! [V: $i] :
( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) )
<=> $true )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [U: $i] :
( ssList(U)
=> ! [V: $i] :
( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) )
<=> ! [U: $i] : $true ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [U: $i] :
( ssList(U)
=> ! [V: $i] :
( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
( ~ ! [U: $i] :
( ssList(U)
=> ! [V: $i] :
( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ~ ! [U: $i] :
( ssList(U)
=> ! [V: $i] :
( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) )
<=> $false ),
inference(transitivity,[status(thm)],[6,1]) ).
tff(8,axiom,
~ ! [U: $i] :
( ssList(U)
=> ! [V: $i] :
( ssList(V)
=> ! [W: $i] :
( ssList(W)
=> ! [X: $i] :
( ssList(X)
=> ( ( V != X )
| ( U != W )
| ( ( ~ neq(V,nil)
| ~ singletonP(W)
| singletonP(U) )
& ( ~ neq(V,nil)
| neq(X,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(9,plain,
$false,
inference(modus_ponens,[status(thm)],[8,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC255+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 : Fri Jun 20 08:46:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------