%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET014-2 : 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 08:35:17 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 10 !; 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_union_is_member_of_one_set,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| member(VAR_0,VAR_1)
| ~ member(VAR_0,union(VAR_1,VAR_2)) ),
file('theBenchmark.p',member_of_union_is_member_of_one_set) ).
cnf(c_9,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[member_of_union_is_member_of_one_set]) ).
fof(a_subset_of_c,axiom,
subset(as,cs),
file('theBenchmark.p',a_subset_of_c) ).
cnf(c_22,plain,
subset(as,cs),
inference(clausify,[status(thm)],[a_subset_of_c]) ).
fof(b_subset_of_c,axiom,
subset(bs,cs),
file('theBenchmark.p',b_subset_of_c) ).
cnf(c_23,plain,
subset(bs,cs),
inference(clausify,[status(thm)],[b_subset_of_c]) ).
fof(prove_a_union_b_subset_of_c,axiom,
~ subset(union(as,bs),cs),
file('theBenchmark.p',prove_a_union_b_subset_of_c) ).
cnf(c_24,plain,
~ subset(union(as,bs),cs),
inference(clausify,[status(thm)],[prove_a_union_b_subset_of_c]) ).
cnf(c_44,plain,
( member(A,cs)
| ~ member(A,as) ),
inference(resolve,[status(thm)],[c_22,c_2]) ).
cnf(c_47,plain,
( member(A,cs)
| ~ member(A,bs) ),
inference(resolve,[status(thm)],[c_23,c_2]) ).
cnf(c_48,plain,
member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)),
inference(resolve,[status(thm)],[c_24,c_3]) ).
cnf(c_51,plain,
~ member(member_of_1_not_of_2(union(as,bs),cs),cs),
inference(resolve,[status(thm)],[c_4,c_24]) ).
cnf(c_169,plain,
( member(member_of_1_not_of_2(union(as,bs),cs),bs)
| member(member_of_1_not_of_2(union(as,bs),cs),as) ),
inference(resolve,[status(thm)],[c_48,c_9]) ).
cnf(c_178,plain,
~ member(member_of_1_not_of_2(union(as,bs),cs),bs),
inference(resolve,[status(thm)],[c_47,c_51]) ).
cnf(c_179,plain,
~ member(member_of_1_not_of_2(union(as,bs),cs),as),
inference(resolve,[status(thm)],[c_44,c_51]) ).
cnf(c_202,plain,
member(member_of_1_not_of_2(union(as,bs),cs),bs),
inference(resolve,[status(thm)],[c_179,c_169]) ).
cnf(c_201,plain,
$false,
inference(resolve,[status(thm)],[c_178,c_202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 06:49:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2421996 was started by sandbox on n014,
% 0.09/0.37 % Sat Sep 26 06:49:48 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.40 % Length of proof is 15.
% 0.09/0.40 % Level of proof is 3.
% 0.09/0.40 % Maximum clause weight is 29.000.
% 0.09/0.40 % Given clauses 67.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------