%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:35:17 AM UTC 2026
% Result : Unsatisfiable 7.63s 1.56s
% Output : CNFRefutation 7.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 27 unt; 0 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 40 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(membership_in_subsets,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ subset(VAR_1,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',membership_in_subsets) ).
cnf(c_2,plain,
( member(A,C)
| ~ subset(B,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[membership_in_subsets]) ).
fof(subsets_axiom1,axiom,
! [VAR_0,VAR_1] :
( member(member_of_1_not_of_2(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subsets_axiom1) ).
cnf(c_3,plain,
( member(member_of_1_not_of_2(A,B),A)
| subset(A,B) ),
inference(clausify,[status(thm)],[subsets_axiom1]) ).
fof(subsets_axiom2,axiom,
! [VAR_0,VAR_1] :
( subset(VAR_0,VAR_1)
| ~ member(member_of_1_not_of_2(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',subsets_axiom2) ).
cnf(c_4,plain,
( subset(A,B)
| ~ member(member_of_1_not_of_2(A,B),B) ),
inference(clausify,[status(thm)],[subsets_axiom2]) ).
fof(member_of_both_is_member_of_intersection,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,intersection(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',member_of_both_is_member_of_intersection) ).
cnf(c_10,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[member_of_both_is_member_of_intersection]) ).
fof(member_of_intersection_is_member_of_set1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',member_of_intersection_is_member_of_set1) ).
cnf(c_11,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[member_of_intersection_is_member_of_set1]) ).
fof(member_of_intersection_is_member_of_set2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',member_of_intersection_is_member_of_set2) ).
cnf(c_12,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[member_of_intersection_is_member_of_set2]) ).
fof(set_equal_sets_are_subsets1,axiom,
! [VAR_0,VAR_1] :
( subset(VAR_0,VAR_1)
| ~ equal_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',set_equal_sets_are_subsets1) ).
cnf(c_13,plain,
( subset(A,B)
| ~ equal_sets(A,B) ),
inference(clausify,[status(thm)],[set_equal_sets_are_subsets1]) ).
fof(set_equal_sets_are_subsets2,axiom,
! [VAR_0,VAR_1] :
( subset(VAR_1,VAR_0)
| ~ equal_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',set_equal_sets_are_subsets2) ).
cnf(c_14,plain,
( subset(B,A)
| ~ equal_sets(A,B) ),
inference(clausify,[status(thm)],[set_equal_sets_are_subsets2]) ).
fof(subsets_are_set_equal_sets,axiom,
! [VAR_0,VAR_1] :
( equal_sets(VAR_1,VAR_0)
| ~ subset(VAR_1,VAR_0)
| ~ subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subsets_are_set_equal_sets) ).
cnf(c_15,plain,
( equal_sets(B,A)
| ~ subset(B,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subsets_are_set_equal_sets]) ).
fof(symmetry_for_set_equal,axiom,
! [VAR_0,VAR_1] :
( equal_sets(VAR_1,VAR_0)
| ~ equal_sets(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry_for_set_equal) ).
cnf(c_17,plain,
( equal_sets(B,A)
| ~ equal_sets(A,B) ),
inference(clausify,[status(thm)],[symmetry_for_set_equal]) ).
fof(intersection_of_a_and_b_is_c,axiom,
equal_sets(intersection(as,bs),cs),
file('theBenchmark.p',intersection_of_a_and_b_is_c) ).
cnf(c_22,plain,
equal_sets(intersection(as,bs),cs),
inference(clausify,[status(thm)],[intersection_of_a_and_b_is_c]) ).
fof(intersection_of_b_and_a_is_d,axiom,
equal_sets(intersection(bs,as),ds),
file('theBenchmark.p',intersection_of_b_and_a_is_d) ).
cnf(c_23,plain,
equal_sets(intersection(bs,as),ds),
inference(clausify,[status(thm)],[intersection_of_b_and_a_is_d]) ).
fof(prove_c_equals_d,axiom,
~ equal_sets(cs,ds),
file('theBenchmark.p',prove_c_equals_d) ).
cnf(c_24,plain,
~ equal_sets(cs,ds),
inference(clausify,[status(thm)],[prove_c_equals_d]) ).
cnf(c_41,plain,
( member(member_of_1_not_of_2(B,A),B)
| equal_sets(B,A)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_6061,plain,
( member(member_of_1_not_of_2(B,A),B)
| equal_sets(A,B)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_42,plain,
( member(member_of_1_not_of_2(A,B),A)
| member(member_of_1_not_of_2(B,A),B)
| equal_sets(A,B) ),
inference(resolve,[status(thm)],[c_6061,c_3]) ).
cnf(c_47,plain,
subset(cs,intersection(as,bs)),
inference(resolve,[status(thm)],[c_22,c_14]) ).
cnf(c_48,plain,
subset(intersection(as,bs),cs),
inference(resolve,[status(thm)],[c_22,c_13]) ).
cnf(c_52,plain,
subset(ds,intersection(bs,as)),
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_53,plain,
subset(intersection(bs,as),ds),
inference(resolve,[status(thm)],[c_23,c_13]) ).
cnf(c_55,plain,
~ equal_sets(ds,cs),
inference(resolve,[status(thm)],[c_17,c_24]) ).
cnf(c_83,plain,
( member(A,intersection(as,bs))
| ~ member(A,cs) ),
inference(resolve,[status(thm)],[c_47,c_2]) ).
cnf(c_84,plain,
( member(A,cs)
| ~ member(A,intersection(as,bs)) ),
inference(resolve,[status(thm)],[c_48,c_2]) ).
cnf(c_88,plain,
( member(A,intersection(bs,as))
| ~ member(A,ds) ),
inference(resolve,[status(thm)],[c_52,c_2]) ).
cnf(c_99,plain,
( member(A,ds)
| ~ member(A,intersection(bs,as)) ),
inference(resolve,[status(thm)],[c_53,c_2]) ).
cnf(c_666,plain,
( member(member_of_1_not_of_2(ds,cs),ds)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_42,c_55]) ).
cnf(c_674,plain,
( member(member_of_1_not_of_2(ds,cs),intersection(bs,as))
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_666,c_88]) ).
cnf(c_701,plain,
( member(member_of_1_not_of_2(ds,cs),as)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_674,c_12]) ).
cnf(c_702,plain,
( member(member_of_1_not_of_2(ds,cs),bs)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_674,c_11]) ).
cnf(c_6062,plain,
( member(member_of_1_not_of_2(cs,ds),cs)
| member(member_of_1_not_of_2(ds,cs),intersection(as,A))
| ~ member(member_of_1_not_of_2(ds,cs),A) ),
inference(resolve,[status(thm)],[c_10,c_701]) ).
cnf(c_6063,plain,
( member(member_of_1_not_of_2(cs,ds),cs)
| member(member_of_1_not_of_2(cs,ds),cs)
| member(member_of_1_not_of_2(ds,cs),intersection(as,bs)) ),
inference(resolve,[status(thm)],[c_6062,c_702]) ).
cnf(c_833,plain,
( member(member_of_1_not_of_2(cs,ds),cs)
| member(member_of_1_not_of_2(ds,cs),intersection(as,bs)) ),
inference(copy,[status(thm)],[c_6063]) ).
cnf(c_1366,plain,
( member(member_of_1_not_of_2(ds,cs),cs)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_833,c_84]) ).
cnf(c_1431,plain,
( subset(ds,cs)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_1366,c_4]) ).
cnf(c_6064,plain,
( member(member_of_1_not_of_2(cs,ds),cs)
| equal_sets(cs,ds)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(resolve,[status(thm)],[c_1431,c_41]) ).
cnf(c_6065,plain,
( equal_sets(cs,ds)
| member(member_of_1_not_of_2(cs,ds),cs) ),
inference(copy,[status(thm)],[c_6064]) ).
cnf(c_1482,plain,
member(member_of_1_not_of_2(cs,ds),cs),
inference(resolve,[status(thm)],[c_24,c_6065]) ).
cnf(c_1483,plain,
member(member_of_1_not_of_2(cs,ds),intersection(as,bs)),
inference(resolve,[status(thm)],[c_1482,c_83]) ).
cnf(c_1722,plain,
member(member_of_1_not_of_2(cs,ds),bs),
inference(resolve,[status(thm)],[c_1483,c_12]) ).
cnf(c_1723,plain,
member(member_of_1_not_of_2(cs,ds),as),
inference(resolve,[status(thm)],[c_1483,c_11]) ).
cnf(c_6066,plain,
( member(member_of_1_not_of_2(cs,ds),intersection(bs,A))
| ~ member(member_of_1_not_of_2(cs,ds),A) ),
inference(resolve,[status(thm)],[c_10,c_1722]) ).
cnf(c_1820,plain,
member(member_of_1_not_of_2(cs,ds),intersection(bs,as)),
inference(resolve,[status(thm)],[c_6066,c_1723]) ).
cnf(c_3069,plain,
member(member_of_1_not_of_2(cs,ds),ds),
inference(resolve,[status(thm)],[c_1820,c_99]) ).
cnf(c_3212,plain,
subset(cs,ds),
inference(resolve,[status(thm)],[c_3069,c_4]) ).
cnf(c_6067,plain,
( member(member_of_1_not_of_2(ds,cs),ds)
| equal_sets(ds,cs) ),
inference(resolve,[status(thm)],[c_3212,c_41]) ).
cnf(c_3285,plain,
member(member_of_1_not_of_2(ds,cs),ds),
inference(resolve,[status(thm)],[c_55,c_6067]) ).
cnf(c_6068,plain,
( equal_sets(cs,ds)
| ~ subset(ds,cs) ),
inference(resolve,[status(thm)],[c_3212,c_15]) ).
cnf(c_3286,plain,
~ subset(ds,cs),
inference(resolve,[status(thm)],[c_24,c_6068]) ).
cnf(c_3295,plain,
member(member_of_1_not_of_2(ds,cs),intersection(bs,as)),
inference(resolve,[status(thm)],[c_3285,c_88]) ).
cnf(c_3329,plain,
~ member(member_of_1_not_of_2(ds,cs),cs),
inference(resolve,[status(thm)],[c_4,c_3286]) ).
cnf(c_4386,plain,
~ member(member_of_1_not_of_2(ds,cs),intersection(as,bs)),
inference(resolve,[status(thm)],[c_84,c_3329]) ).
cnf(c_5977,plain,
member(member_of_1_not_of_2(ds,cs),as),
inference(resolve,[status(thm)],[c_3295,c_12]) ).
cnf(c_5978,plain,
member(member_of_1_not_of_2(ds,cs),bs),
inference(resolve,[status(thm)],[c_3295,c_11]) ).
cnf(c_6069,plain,
( member(member_of_1_not_of_2(ds,cs),intersection(as,A))
| ~ member(member_of_1_not_of_2(ds,cs),A) ),
inference(resolve,[status(thm)],[c_10,c_5977]) ).
cnf(c_6070,plain,
member(member_of_1_not_of_2(ds,cs),intersection(as,bs)),
inference(resolve,[status(thm)],[c_6069,c_5978]) ).
cnf(c_6060,plain,
$false,
inference(resolve,[status(thm)],[c_4386,c_6070]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.54 % Computer : n026.cluster.edu
% 0.10/0.54 % Model : x86_64 x86_64
% 0.10/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.54 % Memory : 8046.5625MB
% 0.10/0.54 % OS : Linux 6.8.0-71-generic
% 0.10/0.54 % CPULimit : 300
% 0.10/0.54 % WCLimit : 300
% 0.10/0.54 % DateTime : Sat Sep 26 06:52:28 UTC 2026
% 0.10/0.54 % CPUTime :
% 0.10/0.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.54 % Process 336783 was started by sandbox2 on n026,
% 0.10/0.54 % Sat Sep 26 06:52:28 2026
% 0.10/0.54 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.55
% 0.10/0.55 % From the command line: assign(max_seconds, 300).
% 7.63/1.56
% 7.63/1.56 % Assigning unary symbol complement kb_weight 0 and highest precedence (13).
% 7.63/1.56
% 7.63/1.56 % SZS status Unsatisfiable for theBenchmark
% 7.63/1.56
% 7.63/1.56 % Proof 1 at 0.77 (+ 0.22) seconds.
% 7.63/1.56 % Length of proof is 46.
% 7.63/1.56 % Level of proof is 17.
% 7.63/1.56 % Maximum clause weight is 23.000.
% 7.63/1.56 % Given clauses 285.
% 7.63/1.56
% 7.63/1.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------