%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET012-1 : 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 : n009.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 0.99s 0.61s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(prove_involution,axiom,
~ equal_sets(complement(complement(a)),a),
file('theBenchmark.p',prove_involution) ).
cnf(c_22,plain,
~ equal_sets(complement(complement(a)),a),
inference(clausify,[status(thm)],[prove_involution]) ).
cnf(c_29,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_32,plain,
( subset(A,complement(B))
| member(member_of_1_not_of_2(A,complement(B)),B) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_37,plain,
( subset(A,B)
| ~ member(member_of_1_not_of_2(A,B),complement(A)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_39,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_65,plain,
~ equal_sets(a,complement(complement(a))),
inference(resolve,[status(thm)],[c_17,c_22]) ).
cnf(c_1501,plain,
( subset(A,complement(complement(A)))
| subset(A,complement(complement(A))) ),
inference(resolve,[status(thm)],[c_37,c_32]) ).
cnf(c_239,plain,
subset(A,complement(complement(A))),
inference(copy,[status(thm)],[c_1501]) ).
cnf(c_1502,plain,
( subset(complement(complement(A)),A)
| subset(complement(complement(A)),A) ),
inference(resolve,[status(thm)],[c_39,c_29]) ).
cnf(c_312,plain,
subset(complement(complement(A)),A),
inference(copy,[status(thm)],[c_1502]) ).
cnf(c_1503,plain,
( equal_sets(A,complement(complement(A)))
| ~ subset(complement(complement(A)),A) ),
inference(resolve,[status(thm)],[c_239,c_15]) ).
cnf(c_1499,plain,
equal_sets(A,complement(complement(A))),
inference(resolve,[status(thm)],[c_312,c_1503]) ).
cnf(c_1500,plain,
$false,
inference(resolve,[status(thm)],[c_1499,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 06:49:14 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3591994 was started by sandbox on n009,
% 0.13/0.36 % Sat Sep 26 06:49:14 2026
% 0.13/0.36 % 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).
% 0.99/0.61
% 0.99/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.99/0.61
% 0.99/0.61 % Proof 1 at 0.13 (+ 0.05) seconds.
% 0.99/0.61 % Length of proof is 16.
% 0.99/0.61 % Level of proof is 4.
% 0.99/0.61 % Maximum clause weight is 16.000.
% 0.99/0.61 % Given clauses 175.
% 0.99/0.61
% 0.99/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------