%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET009-1 : 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 : n015.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 08:35:15 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 32 ~; 28 |; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 2 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d_is_a_subset_of_a,axiom,
subset(d,a),
file('theBenchmark.p',d_is_a_subset_of_a) ).
cnf(c_4,plain,
subset(d,a),
inference(clausify,[status(thm)],[d_is_a_subset_of_a]) ).
fof(prove_bDa_is_a_subset_of_bDd,axiom,
~ subset(bDa,bDd),
file('theBenchmark.p',prove_bDa_is_a_subset_of_bDd) ).
cnf(c_5,plain,
~ subset(bDa,bDd),
inference(clausify,[status(thm)],[prove_bDa_is_a_subset_of_bDd]) ).
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_6,plain,
( subset(A,B)
| ~ member(member_of_1_not_of_2(A,B),B) ),
inference(clausify,[status(thm)],[subsets_axiom2]) ).
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_7,plain,
( member(member_of_1_not_of_2(A,B),A)
| subset(A,B) ),
inference(clausify,[status(thm)],[subsets_axiom1]) ).
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_8,plain,
( member(A,C)
| ~ subset(B,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[membership_in_subsets]) ).
fof(member_of_difference_or_set2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_0,VAR_2)
| member(VAR_0,VAR_3)
| ~ difference(VAR_1,VAR_2,VAR_3)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',member_of_difference_or_set2) ).
cnf(c_10,plain,
( member(A,C)
| member(A,D)
| ~ difference(B,C,D)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[member_of_difference_or_set2]) ).
fof(not_member_of_difference,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ difference(VAR_3,VAR_1,VAR_2)
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',not_member_of_difference) ).
cnf(c_11,plain,
( ~ difference(D,B,C)
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[not_member_of_difference]) ).
fof(member_of_difference,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ difference(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_difference) ).
cnf(c_12,plain,
( member(D,A)
| ~ member(D,C)
| ~ difference(A,B,C) ),
inference(clausify,[status(thm)],[member_of_difference]) ).
fof(b_minus_a,axiom,
difference(b,a,bDa),
file('theBenchmark.p',b_minus_a) ).
cnf(c_15,plain,
difference(b,a,bDa),
inference(clausify,[status(thm)],[b_minus_a]) ).
fof(b_minus_d,axiom,
difference(b,d,bDd),
file('theBenchmark.p',b_minus_d) ).
cnf(c_16,plain,
difference(b,d,bDd),
inference(clausify,[status(thm)],[b_minus_d]) ).
cnf(c_19,plain,
( member(A,d)
| member(A,bDd)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_20,plain,
( member(A,b)
| ~ member(A,bDa) ),
inference(resolve,[status(thm)],[c_15,c_12]) ).
cnf(c_21,plain,
( ~ member(A,bDa)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_32,plain,
~ member(member_of_1_not_of_2(bDa,bDd),bDd),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_33,plain,
member(member_of_1_not_of_2(bDa,bDd),bDa),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_36,plain,
( member(A,a)
| ~ member(A,d) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_54,plain,
member(member_of_1_not_of_2(bDa,bDd),b),
inference(resolve,[status(thm)],[c_33,c_20]) ).
cnf(c_55,plain,
~ member(member_of_1_not_of_2(bDa,bDd),a),
inference(resolve,[status(thm)],[c_21,c_33]) ).
cnf(c_180,plain,
~ member(member_of_1_not_of_2(bDa,bDd),d),
inference(resolve,[status(thm)],[c_36,c_55]) ).
cnf(c_188,plain,
( member(member_of_1_not_of_2(bDa,bDd),d)
| ~ member(member_of_1_not_of_2(bDa,bDd),b) ),
inference(resolve,[status(thm)],[c_19,c_32]) ).
cnf(c_189,plain,
~ member(member_of_1_not_of_2(bDa,bDd),b),
inference(resolve,[status(thm)],[c_188,c_180]) ).
cnf(c_187,plain,
$false,
inference(resolve,[status(thm)],[c_54,c_189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 06:51:43 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 3368929 was started by sandbox on n015,
% 0.09/0.37 % Sat Sep 26 06:51:43 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.42
% 0.09/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.42
% 0.09/0.42 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.42 % Length of proof is 20.
% 0.09/0.42 % Level of proof is 4.
% 0.09/0.42 % Maximum clause weight is 9.000.
% 0.09/0.42 % Given clauses 28.
% 0.09/0.42
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------