%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET001-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:24:43 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 34 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 161 ( 76 ~; 72 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 77 ( 69 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
tff(subset_type,type,
subset: ( $i * $i ) > $o ).
tff(bb_type,type,
bb: $i ).
tff(b_type,type,
b: $i ).
tff(equal_sets_type,type,
equal_sets: ( $i * $i ) > $o ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(element_of_b_type,type,
element_of_b: $i ).
tff(1,plain,
( equal_sets(b,bb)
<=> equal_sets(b,bb) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
equal_sets(b,bb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_equals_bb) ).
tff(3,plain,
equal_sets(b,bb),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Subset: $i,Superset: $i] :
refl(( ( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) )
<=> ( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) )
<=> ! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) )
<=> ! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',set_equal_sets_are_subsets1) ).
tff(8,plain,
! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) )
| ~ equal_sets(b,bb)
| subset(b,bb) )
<=> ( ~ ! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) )
| ~ equal_sets(b,bb)
| subset(b,bb) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) )
| ~ equal_sets(b,bb)
| subset(b,bb) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Subset: $i,Superset: $i] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) )
| ~ equal_sets(b,bb)
| subset(b,bb) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
subset(b,bb),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ member(element_of_b,bb)
<=> ~ member(element_of_b,bb) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
~ member(element_of_b,bb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_element_of_bb) ).
tff(17,plain,
~ member(element_of_b,bb),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( member(element_of_b,b)
<=> member(element_of_b,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
member(element_of_b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_of_b) ).
tff(20,plain,
member(element_of_b,b),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [Subset: $i,Element: $i,Superset: $i] :
refl(( ( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
<=> ( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
<=> ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
<=> ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [Subset: $i,Element: $i,Superset: $i] :
rewrite(( ( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) )
<=> ( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [Subset: $i,Element: $i,Superset: $i] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) )
<=> ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [Subset: $i,Element: $i,Superset: $i] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).
tff(27,plain,
! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(element_of_b,bb)
| ~ subset(b,bb)
| ~ member(element_of_b,b) )
<=> ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(element_of_b,bb)
| ~ subset(b,bb)
| ~ member(element_of_b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(element_of_b,bb)
| ~ subset(b,bb)
| ~ member(element_of_b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(element_of_b,bb)
| ~ subset(b,bb)
| ~ member(element_of_b,b) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET001-1 : TPTP v9.0.0. Released v1.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 04:00:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------