%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET001-1 : 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 : n011.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 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 11 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_3,plain,
( subset(A,B)
| ~ equal_sets(A,B) ),
inference(clausify,[status(thm)],[set_equal_sets_are_subsets1]) ).
fof(b_equals_bb,axiom,
equal_sets(b,bb),
file('theBenchmark.p',b_equals_bb) ).
cnf(c_4,plain,
equal_sets(b,bb),
inference(clausify,[status(thm)],[b_equals_bb]) ).
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_5,plain,
( member(A,C)
| ~ subset(B,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[membership_in_subsets]) ).
cnf(c_9,plain,
subset(b,bb),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_10,plain,
( member(A,bb)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_5,c_9]) ).
fof(element_of_b,axiom,
member(element_of_b,b),
file('theBenchmark.p',element_of_b) ).
cnf(c_14,plain,
member(element_of_b,b),
inference(clausify,[status(thm)],[element_of_b]) ).
fof(prove_element_of_bb,axiom,
~ member(element_of_b,bb),
file('theBenchmark.p',prove_element_of_bb) ).
cnf(c_15,plain,
~ member(element_of_b,bb),
inference(clausify,[status(thm)],[prove_element_of_bb]) ).
cnf(c_19,plain,
member(element_of_b,bb),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_18,plain,
$false,
inference(resolve,[status(thm)],[c_15,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 06:46:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 4006650 was started by sandbox on n011,
% 0.10/0.38 % Sat Sep 26 06:46:58 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 8.
% 0.10/0.39 % Level of proof is 3.
% 0.10/0.39 % Maximum clause weight is 6.000.
% 0.10/0.39 % Given clauses 5.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------