%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET006-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:24:44 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 20
% Syntax : Number of formulae : 42 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 216 ( 93 ~; 104 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 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 : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 120 ( 108 !; 0 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(member_of_1_not_of_2_type,type,
member_of_1_not_of_2: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i ).
tff(subset_type,type,
subset: ( $i * $i ) > $o ).
tff(intersection_type,type,
intersection: ( $i * $i * $i ) > $o ).
tff(1,plain,
( ~ subset(d,a)
<=> ~ subset(d,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ subset(d,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_a_subset_of_a) ).
tff(3,plain,
~ subset(d,a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Subset: $i,Superset: $i] :
refl(( ( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
<=> ( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
<=> ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
<=> ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).
tff(8,plain,
! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
| ~ member(member_of_1_not_of_2(d,a),a)
| subset(d,a) )
<=> ( ~ ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
| ~ member(member_of_1_not_of_2(d,a),a)
| subset(d,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
| ~ member(member_of_1_not_of_2(d,a),a)
| subset(d,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
| ~ member(member_of_1_not_of_2(d,a),a)
| subset(d,a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ member(member_of_1_not_of_2(d,a),a),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [Subset: $i,Superset: $i] :
refl(( ( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
<=> ( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
<=> ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
<=> ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).
tff(19,plain,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(d,a)
| member(member_of_1_not_of_2(d,a),d) )
<=> ( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(d,a)
| member(member_of_1_not_of_2(d,a),d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(d,a)
| member(member_of_1_not_of_2(d,a),d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(d,a)
| member(member_of_1_not_of_2(d,a),d) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
member(member_of_1_not_of_2(d,a),d),
inference(unit_resolution,[status(thm)],[24,21,3]) ).
tff(26,plain,
( intersection(d,a,d)
<=> intersection(d,a,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
intersection(d,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_intersection_a_is_d) ).
tff(28,plain,
intersection(d,a,d),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
^ [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
refl(( ( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) )
<=> ( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) )
<=> ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) )
<=> ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
trans(monotonicity(rewrite(( ( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection) )
<=> ( ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ) )),
( ( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set2) )
<=> ( ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection)
| member(Element,Set2) ) )),
rewrite(( ( ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection)
| member(Element,Set2) )
<=> ( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ) )),
( ( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set2) )
<=> ( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set2) )
<=> ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set2) ).
tff(35,plain,
! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) )
| member(member_of_1_not_of_2(d,a),a)
| ~ member(member_of_1_not_of_2(d,a),d)
| ~ intersection(d,a,d) )
<=> ( ~ ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) )
| member(member_of_1_not_of_2(d,a),a)
| ~ member(member_of_1_not_of_2(d,a),d)
| ~ intersection(d,a,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) )
| member(member_of_1_not_of_2(d,a),a)
| ~ member(member_of_1_not_of_2(d,a),d)
| ~ intersection(d,a,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [Set1: $i,Set2: $i,Element: $i,Intersection: $i] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) )
| member(member_of_1_not_of_2(d,a),a)
| ~ member(member_of_1_not_of_2(d,a),d)
| ~ intersection(d,a,d) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
$false,
inference(unit_resolution,[status(thm)],[41,38,28,25,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET006-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.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 04:01:09 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% See solution above
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------