%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU284+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:27:29 AM UTC 2025
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 326 ( 130 equ)
% Maximal formula atoms : 16 ( 40 avg)
% Number of connectives : 294 ( 60 ~; 31 |; 132 &)
% ( 42 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 84 ( 84 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 : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 127 ( 103 !; 16 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
tff(singleton_type,type,
singleton: $i > $i ).
tff(apply_type,type,
apply: ( $i * $i ) > $i ).
tff(in_type,type,
in: ( $i * $i ) > $o ).
tff(relation_dom_type,type,
relation_dom: $i > $i ).
tff(function_type,type,
function: $i > $o ).
tff(relation_type,type,
relation: $i > $o ).
tff(1,plain,
( ~ ! [A: $i] :
? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) ) )
<=> ~ ! [A: $i] :
? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ ! [A: $i] :
? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
tff(3,plain,
~ ! [A: $i] :
? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [A: $i] :
trans(monotonicity(trans(monotonicity(trans(quant_intro(proof_bind(^ [B: $i,C: $i,D: $i] :
trans(monotonicity(rewrite(( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
<=> ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) ) )),
( ( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
<=> ( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) ) )),
rewrite(( ( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
<=> ( ~ ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
| ( C = D ) ) )),
( ( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
<=> ( ~ ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
| ( C = D ) ) ))),
( ! [B: $i,C: $i,D: $i] :
( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
<=> ! [B: $i,C: $i,D: $i] :
( ~ ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
| ( C = D ) ) )),
trans(trans(der(( ! [B: $i,C: $i,D: $i] :
( ~ ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
| ( C = D ) )
<=> ! [B: $i,C: $i,D: $i] :
( ( singleton(B) = singleton(B) )
| ~ in(B,A) ) )),
elim_unused(( ! [B: $i,C: $i,D: $i] :
( ( singleton(B) = singleton(B) )
| ~ in(B,A) )
<=> ! [B: $i] :
( ( singleton(B) = singleton(B) )
| ~ in(B,A) ) )),
( ! [B: $i,C: $i,D: $i] :
( ~ ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
| ( C = D ) )
<=> ! [B: $i] :
( ( singleton(B) = singleton(B) )
| ~ in(B,A) ) )),
trans(quant_intro(proof_bind(^ [B: $i] :
trans(monotonicity(rewrite(( ( singleton(B) = singleton(B) )
<=> $true )),
( ( ( singleton(B) = singleton(B) )
| ~ in(B,A) )
<=> ( $true
| ~ in(B,A) ) )),
rewrite(( ( $true
| ~ in(B,A) )
<=> $true )),
( ( ( singleton(B) = singleton(B) )
| ~ in(B,A) )
<=> $true ))),
( ! [B: $i] :
( ( singleton(B) = singleton(B) )
| ~ in(B,A) )
<=> ! [B: $i] : $true )),
elim_unused(( ! [B: $i] : $true
<=> $true )),
( ! [B: $i] :
( ( singleton(B) = singleton(B) )
| ~ in(B,A) )
<=> $true )),
( ! [B: $i,C: $i,D: $i] :
( ~ ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
| ( C = D ) )
<=> $true )),
( ! [B: $i,C: $i,D: $i] :
( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
<=> $true )),
trans(quant_intro(proof_bind(^ [B: $i] :
trans(monotonicity(trans(monotonicity(der(( ! [C: $i] : ( C != singleton(B) )
<=> $false )),
( ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) )
<=> ( in(B,A)
& $false ) )),
rewrite(( ( in(B,A)
& $false )
<=> $false )),
( ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) )
<=> $false )),
( ~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) )
<=> ~ $false )),
rewrite(( ~ $false
<=> $true )),
( ~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) )
<=> $true ))),
( ! [B: $i] :
~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) )
<=> ! [B: $i] : $true )),
elim_unused(( ! [B: $i] : $true
<=> $true )),
( ! [B: $i] :
~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) )
<=> $true )),
( ( ! [B: $i,C: $i,D: $i] :
( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) ) )
<=> ( $true
& $true ) )),
rewrite(( ( $true
& $true )
<=> $true )),
( ( ! [B: $i,C: $i,D: $i] :
( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) ) )
<=> $true )),
quant_intro(proof_bind(^ [B: $i] :
trans(monotonicity(rewrite(( ( relation(B)
& function(B)
& ( relation_dom(B) = A ) )
<=> ( relation(B)
& function(B)
& ( relation_dom(B) = A ) ) )),
quant_intro(proof_bind(^ [C: $i] :
rewrite(( ( in(C,A)
=> ( apply(B,C) = singleton(C) ) )
<=> ( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ))),
( ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) )
<=> ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) )),
( ( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) ) )
<=> ( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) )),
rewrite(( ( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) )
<=> ( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) )),
( ( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) ) )
<=> ( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) ))),
( ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) ) )
<=> ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) )),
( ( ( ! [B: $i,C: $i,D: $i] :
( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) ) )
=> ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) ) ) )
<=> ( $true
=> ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) ) )),
rewrite(( ( $true
=> ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) )
<=> ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) )),
( ( ( ! [B: $i,C: $i,D: $i] :
( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) ) )
=> ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) ) ) )
<=> ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) ) )
=> ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) ) ) )
<=> ! [A: $i] :
? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( in(B,A)
& ( C = singleton(B) )
& ( D = singleton(B) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( in(B,A)
& ! [C: $i] : ( C != singleton(B) ) ) )
=> ? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( in(C,A)
=> ( apply(B,C) = singleton(C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
tff(7,plain,
! [A: $i] :
? [B: $i] :
( relation(B)
& function(B)
& ( relation_dom(B) = A )
& ! [C: $i] :
( ~ in(C,A)
| ( apply(B,C) = singleton(C) ) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
$false,
inference(unit_resolution,[status(thm)],[7,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU284+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n009.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 06:35:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% See solution above
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------