%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM183-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:18:52 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 32
% Syntax : Number of formulae : 74 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 334 ( 4 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 440 ( 193 ~; 210 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 166 ( 149 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(universal_class_type,type,
universal_class: $i ).
tff(ordinal_numbers_type,type,
ordinal_numbers: $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(kind_1_ordinals_type,type,
kind_1_ordinals: $i ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(limit_ordinals_type,type,
limit_ordinals: $i ).
tff(1,plain,
( ( intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals )
<=> ( intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',limit_ordinals) ).
tff(3,plain,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( member(x,intersection(complement(kind_1_ordinals),ordinal_numbers))
<=> member(x,limit_ordinals) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( member(x,limit_ordinals)
<=> member(x,intersection(complement(kind_1_ordinals),ordinal_numbers)) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ~ member(x,limit_ordinals)
<=> ~ member(x,intersection(complement(kind_1_ordinals),ordinal_numbers)) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ~ member(x,limit_ordinals)
<=> ~ member(x,limit_ordinals) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
~ member(x,limit_ordinals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordinals_are_kind_1_or_limit_3) ).
tff(9,plain,
~ member(x,limit_ordinals),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
~ member(x,intersection(complement(kind_1_ordinals),ordinal_numbers)),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( member(x,ordinal_numbers)
<=> member(x,ordinal_numbers) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
member(x,ordinal_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordinals_are_kind_1_or_limit_1) ).
tff(13,plain,
member(x,ordinal_numbers),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
<=> ( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) )
<=> ( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
tff(20,plain,
! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
| member(x,intersection(complement(kind_1_ordinals),ordinal_numbers))
| ~ member(x,ordinal_numbers)
| ~ member(x,complement(kind_1_ordinals)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
| member(x,intersection(complement(kind_1_ordinals),ordinal_numbers))
| ~ member(x,ordinal_numbers)
| ~ member(x,complement(kind_1_ordinals)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
| member(x,intersection(complement(kind_1_ordinals),ordinal_numbers))
| ~ member(x,ordinal_numbers)
| ~ member(x,complement(kind_1_ordinals)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
| member(x,intersection(complement(kind_1_ordinals),ordinal_numbers))
| ~ member(x,ordinal_numbers)
| ~ member(x,complement(kind_1_ordinals)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( member(x,intersection(complement(kind_1_ordinals),ordinal_numbers))
| ~ member(x,complement(kind_1_ordinals)) ),
inference(unit_resolution,[status(thm)],[26,23,13]) ).
tff(28,plain,
~ member(x,complement(kind_1_ordinals)),
inference(unit_resolution,[status(thm)],[27,10]) ).
tff(29,plain,
( ~ member(x,kind_1_ordinals)
<=> ~ member(x,kind_1_ordinals) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ member(x,kind_1_ordinals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordinals_are_kind_1_or_limit_2) ).
tff(31,plain,
~ member(x,kind_1_ordinals),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [Z: $i,X: $i] :
refl(( ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
<=> ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [Z: $i,X: $i] :
rewrite(( ( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) )
<=> ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) )
<=> ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [Z: $i,X: $i] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
tff(38,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(x,kind_1_ordinals)
| member(x,complement(kind_1_ordinals))
| ~ member(x,universal_class) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(x,kind_1_ordinals)
| member(x,complement(kind_1_ordinals))
| ~ member(x,universal_class) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( member(x,kind_1_ordinals)
| ~ member(x,universal_class)
| member(x,complement(kind_1_ordinals)) )
<=> ( member(x,kind_1_ordinals)
| member(x,complement(kind_1_ordinals))
| ~ member(x,universal_class) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(x,kind_1_ordinals)
| ~ member(x,universal_class)
| member(x,complement(kind_1_ordinals)) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(x,kind_1_ordinals)
| member(x,complement(kind_1_ordinals))
| ~ member(x,universal_class) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(x,kind_1_ordinals)
| ~ member(x,universal_class)
| member(x,complement(kind_1_ordinals)) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(x,kind_1_ordinals)
| member(x,complement(kind_1_ordinals))
| ~ member(x,universal_class) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(x,kind_1_ordinals)
| ~ member(x,universal_class)
| member(x,complement(kind_1_ordinals)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(x,kind_1_ordinals)
| member(x,complement(kind_1_ordinals))
| ~ member(x,universal_class) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ member(x,universal_class),
inference(unit_resolution,[status(thm)],[47,41,31,28]) ).
tff(49,plain,
^ [Y: $i,U: $i,X: $i] :
refl(( ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
<=> ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [Y: $i,U: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ subclass(X,Y)
| ~ member(U,X) )
<=> ( ~ member(U,X)
| ~ subclass(X,Y) ) )),
( ( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) )
<=> ( ~ member(U,X)
| ~ subclass(X,Y)
| member(U,Y) ) )),
rewrite(( ( ~ member(U,X)
| ~ subclass(X,Y)
| member(U,Y) )
<=> ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) )),
( ( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) )
<=> ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [Y: $i,U: $i,X: $i] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [Y: $i,U: $i,X: $i] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
tff(55,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(x,ordinal_numbers)
| member(x,universal_class)
| ~ subclass(ordinal_numbers,universal_class) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(x,ordinal_numbers)
| member(x,universal_class)
| ~ subclass(ordinal_numbers,universal_class) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( member(x,universal_class)
| ~ member(x,ordinal_numbers)
| ~ subclass(ordinal_numbers,universal_class) )
<=> ( ~ member(x,ordinal_numbers)
| member(x,universal_class)
| ~ subclass(ordinal_numbers,universal_class) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(x,universal_class)
| ~ member(x,ordinal_numbers)
| ~ subclass(ordinal_numbers,universal_class) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(x,ordinal_numbers)
| member(x,universal_class)
| ~ subclass(ordinal_numbers,universal_class) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(x,universal_class)
| ~ member(x,ordinal_numbers)
| ~ subclass(ordinal_numbers,universal_class) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(x,ordinal_numbers)
| member(x,universal_class)
| ~ subclass(ordinal_numbers,universal_class) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(x,universal_class)
| ~ member(x,ordinal_numbers)
| ~ subclass(ordinal_numbers,universal_class) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(x,ordinal_numbers)
| member(x,universal_class)
| ~ subclass(ordinal_numbers,universal_class) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
~ subclass(ordinal_numbers,universal_class),
inference(unit_resolution,[status(thm)],[64,58,13,48]) ).
tff(66,plain,
^ [X: $i] :
refl(( subclass(X,universal_class)
<=> subclass(X,universal_class) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X: $i] : subclass(X,universal_class)
<=> ! [X: $i] : subclass(X,universal_class) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X: $i] : subclass(X,universal_class)
<=> ! [X: $i] : subclass(X,universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
! [X: $i] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
tff(70,plain,
! [X: $i] : subclass(X,universal_class),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [X: $i] : subclass(X,universal_class),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [X: $i] : subclass(X,universal_class),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [X: $i] : subclass(X,universal_class)
| subclass(ordinal_numbers,universal_class) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,72,65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM183-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.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 00:24:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47 % SZS output start Proof
% See solution above
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------