%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:35:16 AM UTC 2026
% Result : Unsatisfiable 3.78s 1.03s
% Output : CNFRefutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 18 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 34 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 19 !; 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_set_or_complement,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,complement(VAR_1))
| member(VAR_0,VAR_1) ),
file('theBenchmark.p',member_of_set_or_complement) ).
cnf(c_5,plain,
( member(A,complement(B))
| member(A,B) ),
inference(clausify,[status(thm)],[member_of_set_or_complement]) ).
fof(not_member_of_set_and_complement,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,complement(VAR_1))
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',not_member_of_set_and_complement) ).
cnf(c_6,plain,
( ~ member(A,complement(B))
| ~ member(A,B) ),
inference(clausify,[status(thm)],[not_member_of_set_and_complement]) ).
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(complement_of_a_is_b,axiom,
equal_sets(complement(a),b),
file('theBenchmark.p',complement_of_a_is_b) ).
cnf(c_22,plain,
equal_sets(complement(a),b),
inference(clausify,[status(thm)],[complement_of_a_is_b]) ).
fof(complement_of_b_is_c,axiom,
equal_sets(complement(b),c),
file('theBenchmark.p',complement_of_b_is_c) ).
cnf(c_23,plain,
equal_sets(complement(b),c),
inference(clausify,[status(thm)],[complement_of_b_is_c]) ).
fof(prove_a_equals_c,axiom,
~ equal_sets(a,c),
file('theBenchmark.p',prove_a_equals_c) ).
cnf(c_24,plain,
~ equal_sets(a,c),
inference(clausify,[status(thm)],[prove_a_equals_c]) ).
cnf(c_30,plain,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),complement(B)) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_34,plain,
( subset(complement(A),B)
| ~ member(member_of_1_not_of_2(complement(A),B),A) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_59,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_63,plain,
subset(b,complement(a)),
inference(resolve,[status(thm)],[c_22,c_14]) ).
cnf(c_64,plain,
subset(complement(a),b),
inference(resolve,[status(thm)],[c_22,c_13]) ).
cnf(c_68,plain,
subset(c,complement(b)),
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_69,plain,
subset(complement(b),c),
inference(resolve,[status(thm)],[c_23,c_13]) ).
cnf(c_71,plain,
~ equal_sets(c,a),
inference(resolve,[status(thm)],[c_17,c_24]) ).
cnf(c_103,plain,
( member(A,complement(a))
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_63,c_2]) ).
cnf(c_142,plain,
( member(A,b)
| ~ member(A,complement(a)) ),
inference(resolve,[status(thm)],[c_64,c_2]) ).
cnf(c_145,plain,
( member(A,complement(b))
| ~ member(A,c) ),
inference(resolve,[status(thm)],[c_68,c_2]) ).
cnf(c_146,plain,
( member(A,c)
| ~ member(A,complement(b)) ),
inference(resolve,[status(thm)],[c_69,c_2]) ).
cnf(c_433,plain,
( subset(A,a)
| member(member_of_1_not_of_2(A,a),b) ),
inference(resolve,[status(thm)],[c_142,c_30]) ).
cnf(c_455,plain,
( member(A,complement(c))
| member(A,complement(b)) ),
inference(resolve,[status(thm)],[c_145,c_5]) ).
cnf(c_796,plain,
( member(A,b)
| member(A,c) ),
inference(resolve,[status(thm)],[c_146,c_5]) ).
cnf(c_812,plain,
( member(A,complement(a))
| member(A,c) ),
inference(resolve,[status(thm)],[c_796,c_103]) ).
cnf(c_836,plain,
( ~ member(A,a)
| member(A,c) ),
inference(resolve,[status(thm)],[c_812,c_6]) ).
cnf(c_844,plain,
( subset(a,A)
| member(member_of_1_not_of_2(a,A),c) ),
inference(resolve,[status(thm)],[c_836,c_3]) ).
cnf(c_4787,plain,
( subset(complement(b),a)
| subset(complement(b),a) ),
inference(resolve,[status(thm)],[c_433,c_34]) ).
cnf(c_2641,plain,
subset(complement(b),a),
inference(copy,[status(thm)],[c_4787]) ).
cnf(c_2658,plain,
( member(A,a)
| ~ member(A,complement(b)) ),
inference(resolve,[status(thm)],[c_2641,c_2]) ).
cnf(c_3401,plain,
( member(A,a)
| member(A,complement(c)) ),
inference(resolve,[status(thm)],[c_455,c_2658]) ).
cnf(c_3457,plain,
( ~ member(A,c)
| member(A,a) ),
inference(resolve,[status(thm)],[c_3401,c_6]) ).
cnf(c_4788,plain,
( subset(a,c)
| subset(a,c) ),
inference(resolve,[status(thm)],[c_844,c_4]) ).
cnf(c_4717,plain,
subset(a,c),
inference(copy,[status(thm)],[c_4788]) ).
cnf(c_4789,plain,
( member(member_of_1_not_of_2(c,a),c)
| equal_sets(c,a) ),
inference(resolve,[status(thm)],[c_4717,c_59]) ).
cnf(c_4727,plain,
member(member_of_1_not_of_2(c,a),c),
inference(resolve,[status(thm)],[c_71,c_4789]) ).
cnf(c_4790,plain,
( equal_sets(a,c)
| ~ subset(c,a) ),
inference(resolve,[status(thm)],[c_4717,c_15]) ).
cnf(c_4728,plain,
~ subset(c,a),
inference(resolve,[status(thm)],[c_24,c_4790]) ).
cnf(c_4729,plain,
member(member_of_1_not_of_2(c,a),a),
inference(resolve,[status(thm)],[c_4727,c_3457]) ).
cnf(c_4791,plain,
subset(c,a),
inference(resolve,[status(thm)],[c_4729,c_4]) ).
cnf(c_4786,plain,
$false,
inference(resolve,[status(thm)],[c_4728,c_4791]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 06:49:16 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2421172 was started by sandbox on n014,
% 0.08/0.36 % Sat Sep 26 06:49:16 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 3.78/1.03
% 3.78/1.03 % SZS status Unsatisfiable for theBenchmark
% 3.78/1.03
% 3.78/1.03 % Proof 1 at 0.42 (+ 0.16) seconds.
% 3.78/1.03 % Length of proof is 39.
% 3.78/1.03 % Level of proof is 10.
% 3.78/1.03 % Maximum clause weight is 25.000.
% 3.78/1.03 % Given clauses 336.
% 3.78/1.03
% 3.78/1.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------