%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Theorem 9.51s 1.70s
% Output : CNFRefutation 9.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 64 ( 15 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 69 ( 28 ~; 26 |; 11 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 4 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_intersection_difference_empty_set,conjecture,
! [B,C] : intersection(difference(B,C),C) = empty_set,
file('theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(prove_intersection_difference_empty_set_neg,negated_conjecture,
~ ! [B,C] : intersection(difference(B,C),C) = empty_set,
inference(assume_negation,[status(cth)],[prove_intersection_difference_empty_set]) ).
fof(nnf_10,plain,
? [B,C] : intersection(difference(B,C),C) != empty_set,
inference(fof_nnf,[status(thm)],[prove_intersection_difference_empty_set_neg]) ).
fof(sk_prove_intersection_difference_empty_set_neg,plain,
intersection(difference(sK0,sK1),sK1) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_10]) ).
cnf(c_14,negated_conjecture,
intersection(difference(sK0,sK1),sK1) != empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_intersection_difference_empty_set_neg]) ).
fof(nnf_9,plain,
! [B,C] :
( ( ? [D] :
( ( ~ member(D,C)
| ~ member(D,B) )
& ( member(D,C)
| member(D,B) ) )
| C = B )
& ( ! [X0] :
( ( ~ member(X0,C)
| member(X0,B) )
& ( member(X0,C)
| ~ member(X0,B) ) )
| C != B ) ),
inference(fof_nnf,[status(thm)],[equal_member_defn]) ).
fof(sk_equal_member_defn_sk,plain,
! [B,C] :
( ( ( ( ~ member(sK2(B,C),C)
| ~ member(sK2(B,C),B) )
& ( member(sK2(B,C),C)
| member(sK2(B,C),B) ) )
| C = B )
& ( ! [X0] :
( ( ~ member(X0,C)
| member(X0,B) )
& ( member(X0,C)
| ~ member(X0,B) ) )
| C != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(D,sK2(B,C))],[nnf_9]) ).
fof(sk_equal_member_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK2(VAR_1,VAR_0),VAR_0)
| ~ member(sK2(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( member(sK2(VAR_1,VAR_0),VAR_0)
| member(sK2(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,VAR_0)
| member(VAR_2,VAR_1)
| VAR_0 != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_0)
| ~ member(VAR_2,VAR_1)
| VAR_0 != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_equal_member_defn_sk]) ).
cnf(c_16,plain,
( member(sK2(B,A),A)
| member(sK2(B,A),B)
| A = B ),
inference(split_conjunct,[status(thm)],[sk_equal_member_defn]) ).
cnf(c_27,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
cnf(c_29,plain,
( ~ member(A,C)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_32,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_33,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_5078,negated_conjecture,
( member(sK2(empty_set,intersection(difference(sK0,sK1),sK1)),intersection(difference(sK0,sK1),sK1))
| member(sK2(empty_set,intersection(difference(sK0,sK1),sK1)),empty_set) ),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_35,negated_conjecture,
member(sK2(empty_set,intersection(difference(sK0,sK1),sK1)),intersection(difference(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_27,c_5078]) ).
cnf(c_102,plain,
member(sK2(empty_set,intersection(difference(sK0,sK1),sK1)),difference(sK0,sK1)),
inference(resolve,[status(thm)],[c_35,c_33]) ).
cnf(c_103,plain,
member(sK2(empty_set,intersection(difference(sK0,sK1),sK1)),sK1),
inference(resolve,[status(thm)],[c_35,c_32]) ).
cnf(c_5079,plain,
~ member(sK2(empty_set,intersection(difference(sK0,sK1),sK1)),sK1),
inference(resolve,[status(thm)],[c_102,c_29]) ).
cnf(c_5077,plain,
$false,
inference(resolve,[status(thm)],[c_103,c_5079]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.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 06:48:36 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 1041097 was started by sandbox2 on n004,
% 0.10/0.38 % Sat Sep 26 06:48:36 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 9.51/1.70
% 9.51/1.70 % SZS status Theorem for theBenchmark
% 9.51/1.70
% 9.51/1.70 % Proof 1 at 0.90 (+ 0.38) seconds.
% 9.51/1.70 % Length of proof is 15.
% 9.51/1.70 % Level of proof is 4.
% 9.51/1.70 % Maximum clause weight is 33.000.
% 9.51/1.70 % Given clauses 348.
% 9.51/1.70
% 9.51/1.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------