%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET132-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:25:19 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 60
% Syntax : Number of formulae : 153 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 524 ( 55 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 644 ( 283 ~; 301 |; 0 &)
% ( 60 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 298 ( 277 !; 0 ?; 298 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(complement_type,type,
complement: $i > $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(u_type,type,
u: $i ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(null_class_type,type,
null_class: $i ).
tff(set_builder_type,type,
set_builder: ( $i * $i ) > $i ).
tff(union_type,type,
union: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( union(singleton(X),Y) = set_builder(X,Y) )
<=> ( union(singleton(X),Y) = set_builder(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) )
<=> ! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) )
<=> ! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
tff(5,plain,
! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) )
| ( union(singleton(u),null_class) = set_builder(u,null_class) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
union(singleton(u),null_class) = set_builder(u,null_class),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
<=> ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
<=> ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
<=> ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
tff(14,plain,
! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
| ( complement(intersection(complement(singleton(u)),complement(null_class))) = union(singleton(u),null_class) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
complement(intersection(complement(singleton(u)),complement(null_class))) = union(singleton(u),null_class),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
complement(intersection(complement(singleton(u)),complement(null_class))) = set_builder(u,null_class),
inference(transitivity,[status(thm)],[18,9]) ).
tff(20,plain,
( member(u,complement(intersection(complement(singleton(u)),complement(null_class))))
<=> member(u,set_builder(u,null_class)) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( member(u,set_builder(u,null_class))
<=> member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) ),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ~ member(u,set_builder(u,null_class))
<=> ~ member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ~ ! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) )
| ( union(singleton(y),set_builder(u,null_class)) = set_builder(y,set_builder(u,null_class)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
union(singleton(y),set_builder(u,null_class)) = set_builder(y,set_builder(u,null_class)),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
| ( complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class)))) = union(singleton(y),set_builder(u,null_class)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class)))) = union(singleton(y),set_builder(u,null_class)),
inference(unit_resolution,[status(thm)],[25,16]) ).
tff(27,plain,
complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class)))) = set_builder(y,set_builder(u,null_class)),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
( member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class)))))
<=> member(u,set_builder(y,set_builder(u,null_class))) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( member(u,set_builder(y,set_builder(u,null_class)))
<=> member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) ),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ member(u,set_builder(y,set_builder(u,null_class)))
<=> ~ member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] : ( union(singleton(X),Y) = set_builder(X,Y) )
| ( union(singleton(x),set_builder(y,set_builder(u,null_class))) = set_builder(x,set_builder(y,set_builder(u,null_class))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
union(singleton(x),set_builder(y,set_builder(u,null_class))) = set_builder(x,set_builder(y,set_builder(u,null_class))),
inference(unit_resolution,[status(thm)],[31,7]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
| ( complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class))))) = union(singleton(x),set_builder(y,set_builder(u,null_class))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class))))) = union(singleton(x),set_builder(y,set_builder(u,null_class))),
inference(unit_resolution,[status(thm)],[33,16]) ).
tff(35,plain,
complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class))))) = set_builder(x,set_builder(y,set_builder(u,null_class))),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class))))))
<=> member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( member(u,set_builder(x,set_builder(y,set_builder(u,null_class))))
<=> member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) ),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class))))
<=> ~ member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class))))
<=> ~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_triple3_2) ).
tff(41,plain,
~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))),
inference(modus_ponens,[status(thm)],[41,38]) ).
tff(43,plain,
( member(u,universal_class)
<=> member(u,universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_triple3_1) ).
tff(45,plain,
member(u,universal_class),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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(49,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(50,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)],[49]) ).
tff(51,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(52,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ( member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) )
<=> ( ~ member(u,universal_class)
| member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))) ),
inference(unit_resolution,[status(thm)],[61,55,45]) ).
tff(63,plain,
member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class))))),
inference(unit_resolution,[status(thm)],[62,42]) ).
tff(64,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
<=> ( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
tff(68,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(set_builder(y,set_builder(u,null_class)))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(set_builder(y,set_builder(u,null_class)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(set_builder(y,set_builder(u,null_class)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(u,intersection(complement(singleton(x)),complement(set_builder(y,set_builder(u,null_class)))))
| member(u,complement(set_builder(y,set_builder(u,null_class)))) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
member(u,complement(set_builder(y,set_builder(u,null_class)))),
inference(unit_resolution,[status(thm)],[73,70,63]) ).
tff(75,plain,
^ [Z: $i,X: $i] :
refl(( ( ~ member(Z,X)
| ~ member(Z,complement(X)) )
<=> ( ~ member(Z,X)
| ~ member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [Z: $i,X: $i] :
rewrite(( ( ~ member(Z,complement(X))
| ~ member(Z,X) )
<=> ( ~ member(Z,X)
| ~ member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,complement(X))
| ~ member(Z,X) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [Z: $i,X: $i] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
tff(81,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
( ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,set_builder(y,set_builder(u,null_class)))
| ~ member(u,complement(set_builder(y,set_builder(u,null_class)))) )
<=> ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,set_builder(y,set_builder(u,null_class)))
| ~ member(u,complement(set_builder(y,set_builder(u,null_class)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,set_builder(y,set_builder(u,null_class)))
| ~ member(u,complement(set_builder(y,set_builder(u,null_class)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,set_builder(y,set_builder(u,null_class)))
| ~ member(u,complement(set_builder(y,set_builder(u,null_class)))) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
~ member(u,set_builder(y,set_builder(u,null_class))),
inference(unit_resolution,[status(thm)],[87,84,74]) ).
tff(89,plain,
~ member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))),
inference(modus_ponens,[status(thm)],[88,30]) ).
tff(90,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) )
<=> ( ~ member(u,universal_class)
| member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(intersection(complement(singleton(y)),complement(set_builder(u,null_class))))) ),
inference(unit_resolution,[status(thm)],[95,55,45]) ).
tff(97,plain,
member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class)))),
inference(unit_resolution,[status(thm)],[96,89]) ).
tff(98,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(set_builder(u,null_class))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(set_builder(u,null_class))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(set_builder(u,null_class))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(u,intersection(complement(singleton(y)),complement(set_builder(u,null_class))))
| member(u,complement(set_builder(u,null_class))) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
member(u,complement(set_builder(u,null_class))),
inference(unit_resolution,[status(thm)],[100,70,97]) ).
tff(102,plain,
( ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,set_builder(u,null_class))
| ~ member(u,complement(set_builder(u,null_class))) )
<=> ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,set_builder(u,null_class))
| ~ member(u,complement(set_builder(u,null_class))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,set_builder(u,null_class))
| ~ member(u,complement(set_builder(u,null_class))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,set_builder(u,null_class))
| ~ member(u,complement(set_builder(u,null_class))) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
~ member(u,set_builder(u,null_class)),
inference(unit_resolution,[status(thm)],[104,84,101]) ).
tff(106,plain,
~ member(u,complement(intersection(complement(singleton(u)),complement(null_class)))),
inference(modus_ponens,[status(thm)],[105,22]) ).
tff(107,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( member(u,intersection(complement(singleton(u)),complement(null_class)))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) )
<=> ( ~ member(u,universal_class)
| member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(u,intersection(complement(singleton(u)),complement(null_class)))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(u,intersection(complement(singleton(u)),complement(null_class)))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(u,intersection(complement(singleton(u)),complement(null_class)))
| ~ member(u,universal_class)
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| ~ member(u,universal_class)
| member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(intersection(complement(singleton(u)),complement(null_class)))) ),
inference(unit_resolution,[status(thm)],[112,55,45]) ).
tff(114,plain,
member(u,intersection(complement(singleton(u)),complement(null_class))),
inference(unit_resolution,[status(thm)],[113,106]) ).
tff(115,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ( ~ member(Z,intersection(X,Y))
| member(Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
tff(119,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(singleton(u))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(singleton(u))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(singleton(u))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(u,intersection(complement(singleton(u)),complement(null_class)))
| member(u,complement(singleton(u))) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
member(u,complement(singleton(u))),
inference(unit_resolution,[status(thm)],[124,121,114]) ).
tff(126,plain,
^ [X: $i] :
refl(( ( unordered_pair(X,X) = singleton(X) )
<=> ( unordered_pair(X,X) = singleton(X) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
<=> ! [X: $i] : ( unordered_pair(X,X) = singleton(X) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
( ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
<=> ! [X: $i] : ( unordered_pair(X,X) = singleton(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
tff(130,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
( ~ ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
| ( unordered_pair(u,u) = singleton(u) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
unordered_pair(u,u) = singleton(u),
inference(unit_resolution,[status(thm)],[133,132]) ).
tff(135,plain,
singleton(u) = unordered_pair(u,u),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( member(u,singleton(u))
<=> member(u,unordered_pair(u,u)) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( member(u,unordered_pair(u,u))
<=> member(u,singleton(u)) ),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
<=> ( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
( ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,axiom,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
tff(142,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[143,139]) ).
tff(145,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(u,universal_class)
| member(u,unordered_pair(u,u)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(u,universal_class)
| member(u,unordered_pair(u,u)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(u,universal_class)
| member(u,unordered_pair(u,u)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(u,universal_class)
| member(u,unordered_pair(u,u)) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
member(u,unordered_pair(u,u)),
inference(unit_resolution,[status(thm)],[147,144,45]) ).
tff(149,plain,
member(u,singleton(u)),
inference(modus_ponens,[status(thm)],[148,137]) ).
tff(150,plain,
( ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,singleton(u))
| ~ member(u,complement(singleton(u))) )
<=> ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,singleton(u))
| ~ member(u,complement(singleton(u))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,singleton(u))
| ~ member(u,complement(singleton(u))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(u,singleton(u))
| ~ member(u,complement(singleton(u))) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
$false,
inference(unit_resolution,[status(thm)],[152,84,149,125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET132-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:27:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56 % SZS output start Proof
% See solution above
% 0.20/0.58 % E exiting
%------------------------------------------------------------------------------