%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:35:14 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.56s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 1 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(prove_a_is_a_subset_of_aUb,axiom,
~ subset(a,aUb),
file('theBenchmark.p',prove_a_is_a_subset_of_aUb) ).
cnf(c_5,plain,
~ subset(a,aUb),
inference(clausify,[status(thm)],[prove_a_is_a_subset_of_aUb]) ).
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_6,plain,
( member(member_of_1_not_of_2(A,B),A)
| subset(A,B) ),
inference(clausify,[status(thm)],[subsets_axiom1]) ).
fof(member_of_set1_is_member_of_union,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_2)
| ~ member(VAR_3,VAR_0)
| ~ union(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_set1_is_member_of_union) ).
cnf(c_10,plain,
( member(D,C)
| ~ member(D,A)
| ~ union(A,B,C) ),
inference(clausify,[status(thm)],[member_of_set1_is_member_of_union]) ).
fof(a_union_b_is_aUb,axiom,
union(a,b,aUb),
file('theBenchmark.p',a_union_b_is_aUb) ).
cnf(c_14,plain,
union(a,b,aUb),
inference(clausify,[status(thm)],[a_union_b_is_aUb]) ).
cnf(c_16,plain,
( member(A,aUb)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_27,plain,
~ member(member_of_1_not_of_2(a,aUb),aUb),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_28,plain,
member(member_of_1_not_of_2(a,aUb),a),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_40,plain,
~ member(member_of_1_not_of_2(a,aUb),a),
inference(resolve,[status(thm)],[c_16,c_27]) ).
cnf(c_39,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n013.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Sat Sep 26 06:47:21 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.09/0.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.55 % Process 2144824 was started by sandbox on n013,
% 0.09/0.55 % Sat Sep 26 06:47:21 2026
% 0.09/0.55 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.55
% 0.09/0.55 % From the command line: assign(max_seconds, 300).
% 0.14/0.56
% 0.14/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.56
% 0.14/0.56 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.56 % Length of proof is 9.
% 0.14/0.56 % Level of proof is 2.
% 0.14/0.56 % Maximum clause weight is 6.000.
% 0.14/0.56 % Given clauses 13.
% 0.14/0.56
% 0.14/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------