%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET975+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 : 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 08:37:23 AM UTC 2026
% Result : Theorem 0.14s 15.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 8 unt; 0 def)
% Number of atoms : 97 ( 36 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 96 ( 39 ~; 43 |; 9 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 7 sgn 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(l55_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(t128_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( in(B,D)
& A = C ) ),
file('theBenchmark.p',t128_zfmisc_1) ).
fof(t128_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( in(B,D)
& A = C ) ),
inference(assume_negation,[status(cth)],[t128_zfmisc_1]) ).
cnf(c_12,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_13,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_16,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_19,plain,
( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_20,plain,
( in(A,C)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_16,c_19]) ).
cnf(c_21,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_22,plain,
( in(B,D)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_16,c_21]) ).
cnf(c_23,plain,
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_24,plain,
( ~ in(B,D)
| ~ in(A,C)
| in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_16,c_23]) ).
fof(nnf_9,plain,
? [A,B,C,D] :
( ( ~ in(B,D)
| C != A
| ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) )
& ( ( in(B,D)
& C = A )
| in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ) ),
inference(fof_nnf,[status(thm)],[t128_zfmisc_1_neg]) ).
fof(sk_t128_zfmisc_1_neg_sk,plain,
( ( ~ in(sK1,sK3)
| sK2 != sK0
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
& ( ( in(sK1,sK3)
& sK2 = sK0 )
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_9]) ).
fof(sk_t128_zfmisc_1_neg,plain,
( ( ~ in(sK1,sK3)
| sK2 != sK0
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
& ( in(sK1,sK3)
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
& ( sK2 = sK0
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ) ),
inference(cnf_transformation,[status(thm)],[sk_t128_zfmisc_1_neg_sk]) ).
cnf(c_27,negated_conjecture,
( sK2 = sK0
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t128_zfmisc_1_neg]) ).
cnf(c_28,negated_conjecture,
( sK2 = sK0
| in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(singleton(sK2),sK3)) ),
inference(paramod,[status(thm)],[c_16,c_27]) ).
cnf(c_29,negated_conjecture,
( in(sK1,sK3)
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t128_zfmisc_1_neg]) ).
cnf(c_30,negated_conjecture,
( in(sK1,sK3)
| in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(singleton(sK2),sK3)) ),
inference(paramod,[status(thm)],[c_16,c_29]) ).
cnf(c_31,negated_conjecture,
( ~ in(sK1,sK3)
| sK2 != sK0
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t128_zfmisc_1_neg]) ).
cnf(c_32,negated_conjecture,
( ~ in(sK1,sK3)
| sK2 != sK0
| ~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(singleton(sK2),sK3)) ),
inference(paramod,[status(thm)],[c_16,c_31]) ).
cnf(c_36,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_13]) ).
cnf(c_52,plain,
( in(sK0,singleton(sK2))
| sK2 = sK0 ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_198,negated_conjecture,
( in(sK1,sK3)
| in(sK1,sK3) ),
inference(resolve,[status(thm)],[c_30,c_22]) ).
cnf(c_57,negated_conjecture,
in(sK1,sK3),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_58,negated_conjecture,
( sK2 != sK0
| ~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(singleton(sK2),sK3)) ),
inference(resolve,[status(thm)],[c_57,c_32]) ).
cnf(c_68,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_36]) ).
cnf(c_75,plain,
( ~ in(A,B)
| in(unordered_pair(unordered_pair(A,sK1),singleton(A)),cartesian_product2(B,sK3)) ),
inference(resolve,[status(thm)],[c_57,c_24]) ).
cnf(c_199,plain,
( sK0 = A
| singleton(A) != singleton(sK2)
| sK2 = sK0 ),
inference(resolve,[status(thm)],[c_52,c_12]) ).
cnf(c_88,plain,
( sK0 = A
| singleton(sK2) != singleton(A)
| sK2 = sK0 ),
inference(copy,[status(thm)],[c_199]) ).
cnf(c_200,plain,
( sK0 = sK2
| sK2 = sK0 ),
inference(xxres,[status(thm)],[c_88]) ).
cnf(c_201,plain,
( sK2 = sK0
| sK2 = sK0 ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_125,plain,
sK2 = sK0,
inference(copy,[status(thm)],[c_201]) ).
cnf(c_202,negated_conjecture,
( sK2 != sK0
| ~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(singleton(sK0),sK3)) ),
inference(paramod,[status(thm)],[c_125,c_58]) ).
cnf(c_203,negated_conjecture,
( sK0 != sK0
| ~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(singleton(sK0),sK3)) ),
inference(paramod,[status(thm)],[c_125,c_202]) ).
cnf(c_126,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0)),cartesian_product2(singleton(sK0),sK3)),
inference(copy,[status(thm)],[c_203]) ).
cnf(c_196,plain,
in(unordered_pair(unordered_pair(A,sK1),singleton(A)),cartesian_product2(singleton(A),sK3)),
inference(resolve,[status(thm)],[c_75,c_68]) ).
cnf(c_197,plain,
$false,
inference(resolve,[status(thm)],[c_196,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET975+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/15.37 % Computer : n004.cluster.edu
% 0.11/15.37 % Model : x86_64 x86_64
% 0.11/15.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.37 % Memory : 8046.5625MB
% 0.11/15.37 % OS : Linux 6.8.0-71-generic
% 0.11/15.37 % CPULimit : 300
% 0.11/15.37 % WCLimit : 300
% 0.11/15.37 % DateTime : Sat Sep 26 08:28:37 UTC 2026
% 0.11/15.38 % CPUTime :
% 0.11/15.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/15.38 % Process 1242267 was started by sandbox on n004,
% 0.11/15.38 % Sat Sep 26 08:28:37 2026
% 0.11/15.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/15.38
% 0.11/15.38 % From the command line: assign(max_seconds, 300).
% 0.14/15.42
% 0.14/15.42 % SZS status Theorem for theBenchmark
% 0.14/15.42
% 0.14/15.42 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/15.42 % Length of proof is 30.
% 0.14/15.42 % Level of proof is 7.
% 0.14/15.42 % Maximum clause weight is 17.000.
% 0.14/15.42 % Given clauses 60.
% 0.14/15.42
% 0.14/15.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------