%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET900+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 : n026.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 08:37:14 AM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 59 ( 46 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 36 ~; 19 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l45_zfmisc_1,axiom,
! [A,B] :
~ ( ! [C] :
~ ( C != B
& in(C,A) )
& A != empty_set
& A != singleton(B) ),
file('theBenchmark.p',l45_zfmisc_1) ).
fof(t41_zfmisc_1,conjecture,
! [A,B] :
~ ( ! [C] :
~ ( C != B
& in(C,A) )
& A != empty_set
& A != singleton(B) ),
file('theBenchmark.p',t41_zfmisc_1) ).
fof(t41_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
~ ( ! [C] :
~ ( C != B
& in(C,A) )
& A != empty_set
& A != singleton(B) ),
inference(assume_negation,[status(cth)],[t41_zfmisc_1]) ).
fof(nnf_4,plain,
! [A,B] :
( ? [C] :
( C != B
& in(C,A) )
| empty_set = A
| singleton(B) = A ),
inference(fof_nnf,[status(thm)],[l45_zfmisc_1]) ).
fof(sk_l45_zfmisc_1_sk,plain,
! [A,B] :
( ( sK0(A,B) != B
& in(sK0(A,B),A) )
| empty_set = A
| singleton(B) = A ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_4]) ).
fof(sk_l45_zfmisc_1,plain,
( ! [VAR_0,VAR_1] :
( sK0(VAR_1,VAR_0) != VAR_0
| empty_set = VAR_1
| singleton(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_1,VAR_0),VAR_1)
| empty_set = VAR_1
| singleton(VAR_0) = VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_l45_zfmisc_1_sk]) ).
cnf(c_10,plain,
( in(sK0(B,A),B)
| empty_set = B
| singleton(A) = B ),
inference(split_conjunct,[status(thm)],[sk_l45_zfmisc_1]) ).
cnf(c_11,plain,
( sK0(B,A) != A
| empty_set = B
| singleton(A) = B ),
inference(split_conjunct,[status(thm)],[sk_l45_zfmisc_1]) ).
fof(nnf_5,plain,
? [A,B] :
( ! [C] :
( C = B
| ~ in(C,A) )
& empty_set != A
& singleton(B) != A ),
inference(fof_nnf,[status(thm)],[t41_zfmisc_1_neg]) ).
fof(sk_t41_zfmisc_1_neg,plain,
( ! [C] :
( C = sK1
| ~ in(C,sK2) )
& empty_set != sK2
& singleton(sK1) != sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1)],[nnf_5]) ).
cnf(c_12,negated_conjecture,
singleton(sK1) != sK2,
inference(split_conjunct,[status(thm)],[sk_t41_zfmisc_1_neg]) ).
cnf(c_13,negated_conjecture,
empty_set != sK2,
inference(split_conjunct,[status(thm)],[sk_t41_zfmisc_1_neg]) ).
cnf(c_14,negated_conjecture,
sK2 != empty_set,
inference(copy,[status(thm)],[c_13]) ).
cnf(c_15,negated_conjecture,
( A = sK1
| ~ in(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t41_zfmisc_1_neg]) ).
cnf(c_16,negated_conjecture,
( sK1 = A
| ~ in(A,sK2) ),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_24,negated_conjecture,
( sK0(sK2,sK1) != sK1
| empty_set = sK2 ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_25,negated_conjecture,
empty_set != sK2,
inference(copy,[status(thm)],[c_14]) ).
cnf(c_19,negated_conjecture,
sK0(sK2,sK1) != sK1,
inference(resolve,[status(thm)],[c_24,c_25]) ).
cnf(c_26,plain,
sK1 != sK0(sK2,sK1),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_22,negated_conjecture,
~ in(sK0(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_16,c_26]) ).
cnf(c_27,plain,
( empty_set = sK2
| singleton(sK1) = sK2 ),
inference(resolve,[status(thm)],[c_22,c_10]) ).
cnf(c_28,plain,
( sK2 = empty_set
| singleton(sK1) = sK2 ),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_29,negated_conjecture,
sK2 = empty_set,
inference(resolve,[status(thm)],[c_12,c_28]) ).
cnf(c_23,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_14,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET900+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n026.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 08:27:27 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 546851 was started by sandbox on n026,
% 0.17/0.43 % Sat Sep 26 08:27:27 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 12.
% 0.17/0.45 % Level of proof is 5.
% 0.17/0.45 % Maximum clause weight is 12.000.
% 0.17/0.45 % Given clauses 14.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------