%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:37:11 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 83 ( 26 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 103 ( 40 ~; 41 |; 19 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 54 ( 3 sgn 39 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(t2_zfmisc_1,conjecture,
union(empty_set) = empty_set,
file('theBenchmark.p',t2_zfmisc_1) ).
fof(t2_zfmisc_1_neg,negated_conjecture,
union(empty_set) != empty_set,
inference(assume_negation,[status(cth)],[t2_zfmisc_1]) ).
fof(nnf_2,plain,
! [A] :
( ( ? [B] : in(B,A)
| empty_set = A )
& ( ! [X0] : ~ in(X0,A)
| empty_set != A ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(sk_d1_xboole_0_sk,plain,
! [A] :
( ( in(sK0(A),A)
| empty_set = A )
& ( ! [X0] : ~ in(X0,A)
| empty_set != A ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0(A))],[nnf_2]) ).
fof(sk_d1_xboole_0,plain,
( ! [VAR_0] :
( in(sK0(VAR_0),VAR_0)
| empty_set = VAR_0 )
& ! [VAR_0,VAR_1] :
( ~ in(VAR_1,VAR_0)
| empty_set != VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_xboole_0_sk]) ).
cnf(c_8,plain,
( ~ in(B,A)
| empty_set != A ),
inference(split_conjunct,[status(thm)],[sk_d1_xboole_0]) ).
cnf(c_9,plain,
( in(sK0(A),A)
| empty_set = A ),
inference(split_conjunct,[status(thm)],[sk_d1_xboole_0]) ).
fof(nnf_3,plain,
! [A,B] :
( ( ? [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) )
& ( ? [X0] :
( in(X0,A)
& in(C,X0) )
| in(C,B) ) )
| union(A) = B )
& ( ! [X1] :
( ( ! [X3] :
( ~ in(X3,A)
| ~ in(X1,X3) )
| in(X1,B) )
& ( ? [X2] :
( in(X2,A)
& in(X1,X2) )
| ~ in(X1,B) ) )
| union(A) != B ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(sk_d4_tarski_sk,plain,
! [A,B] :
( ( ( ( ! [D] :
( ~ in(D,A)
| ~ in(sK2(A,B),D) )
| ~ in(sK2(A,B),B) )
& ( ( in(sK3(A,B),A)
& in(sK2(A,B),sK3(A,B)) )
| in(sK2(A,B),B) ) )
| union(A) = B )
& ( ! [X1] :
( ( ! [X3] :
( ~ in(X3,A)
| ~ in(X1,X3) )
| in(X1,B) )
& ( ( in(sK1(A,B,X1),A)
& in(X1,sK1(A,B,X1)) )
| ~ in(X1,B) ) )
| union(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(A,B,X1)),skolemize(C,sK2(A,B)),skolemize(X0,sK3(A,B))],[nnf_3]) ).
fof(sk_d4_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(VAR_2,VAR_0)
| ~ in(sK2(VAR_0,VAR_1),VAR_2)
| ~ in(sK2(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK3(VAR_0,VAR_1),VAR_0)
| in(sK2(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK2(VAR_0,VAR_1),sK3(VAR_0,VAR_1))
| in(sK2(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_0)
| ~ in(VAR_2,VAR_3)
| in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK1(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,sK1(VAR_0,VAR_1,VAR_2))
| ~ in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_d4_tarski_sk]) ).
cnf(c_11,plain,
( in(sK1(A,B,C),A)
| ~ in(C,B)
| union(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_19,negated_conjecture,
union(empty_set) != empty_set,
inference(clausify,[status(thm)],[t2_zfmisc_1_neg]) ).
cnf(c_22,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_8]) ).
cnf(c_51,plain,
( in(sK1(B,union(B),A),B)
| ~ in(A,union(B)) ),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_48,plain,
~ in(A,union(empty_set)),
inference(resolve,[status(thm)],[c_51,c_22]) ).
cnf(c_52,plain,
empty_set = union(empty_set),
inference(resolve,[status(thm)],[c_48,c_9]) ).
cnf(c_53,plain,
union(empty_set) = empty_set,
inference(copy,[status(thm)],[c_52]) ).
cnf(c_50,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_19,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.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 08:26:20 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 1249738 was started by sandbox on n002,
% 0.09/0.37 % Sat Sep 26 08:26:20 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).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 10.
% 0.09/0.40 % Level of proof is 4.
% 0.09/0.40 % Maximum clause weight is 13.000.
% 0.09/0.40 % Given clauses 17.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------