%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET146+3 : TPTP v9.3.1. Released v2.2.0.
% 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 08:35:54 AM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 56 ( 16 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 24 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 4 sgn 25 !; 2 ?)
% 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(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_th61,conjecture,
! [B] : intersection(B,empty_set) = empty_set,
file('theBenchmark.p',prove_th61) ).
fof(prove_th61_neg,negated_conjecture,
~ ! [B] : intersection(B,empty_set) = empty_set,
inference(assume_negation,[status(cth)],[prove_th61]) ).
fof(nnf_9,plain,
? [B] : intersection(B,empty_set) != empty_set,
inference(fof_nnf,[status(thm)],[prove_th61_neg]) ).
fof(sk_prove_th61_neg,plain,
intersection(sK0,empty_set) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_9]) ).
cnf(c_13,negated_conjecture,
intersection(sK0,empty_set) != empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_th61_neg]) ).
fof(nnf_8,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(sK1(B,C),C)
| ~ member(sK1(B,C),B) )
& ( member(sK1(B,C),C)
| member(sK1(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,[sK1]),skolemize(D,sK1(B,C))],[nnf_8]) ).
fof(sk_equal_member_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK1(VAR_1,VAR_0),VAR_0)
| ~ member(sK1(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( member(sK1(VAR_1,VAR_0),VAR_0)
| member(sK1(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_15,plain,
( member(sK1(B,A),A)
| member(sK1(B,A),B)
| A = B ),
inference(split_conjunct,[status(thm)],[sk_equal_member_defn]) ).
cnf(c_26,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
cnf(c_28,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_69,negated_conjecture,
empty_set != intersection(sK0,empty_set),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_70,negated_conjecture,
( member(sK1(intersection(sK0,empty_set),empty_set),empty_set)
| member(sK1(intersection(sK0,empty_set),empty_set),intersection(sK0,empty_set)) ),
inference(resolve,[status(thm)],[c_15,c_69]) ).
cnf(c_32,negated_conjecture,
member(sK1(intersection(sK0,empty_set),empty_set),intersection(sK0,empty_set)),
inference(resolve,[status(thm)],[c_26,c_70]) ).
cnf(c_67,plain,
~ member(A,intersection(B,empty_set)),
inference(resolve,[status(thm)],[c_28,c_26]) ).
cnf(c_68,plain,
$false,
inference(resolve,[status(thm)],[c_67,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET146+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 07:13:01 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2485103 was started by sandbox on n014,
% 0.08/0.35 % Sat Sep 26 07:13:01 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 11.
% 0.12/0.37 % Level of proof is 3.
% 0.12/0.37 % Maximum clause weight is 24.000.
% 0.12/0.37 % Given clauses 17.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------