%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU148+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 08:45:10 AM UTC 2026
% Result : Theorem 1.99s 0.78s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 94 ( 72 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 72 ( 21 ~; 40 |; 5 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 1 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(l1_zfmisc_1,axiom,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_zfmisc_1,conjecture,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t6_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
inference(assume_negation,[status(cth)],[t6_zfmisc_1]) ).
fof(nnf_8,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_8]) ).
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_83,plain,
( in(sK0(A),A)
| empty_set = A ),
inference(split_conjunct,[status(thm)],[sk_d1_xboole_0]) ).
cnf(c_88,plain,
( D = B
| D = A
| ~ in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_126,plain,
singleton(A) != empty_set,
inference(clausify,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_132,plain,
( singleton(B) = A
| empty_set = A
| ~ subset(A,singleton(B)) ),
inference(clausify,[status(thm)],[l4_zfmisc_1]) ).
cnf(c_169,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
fof(nnf_69,plain,
? [A,B] :
( B != A
& subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1_neg]) ).
fof(sk_t6_zfmisc_1_neg,plain,
( sK2 != sK1
& subset(singleton(sK1),singleton(sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_69]) ).
cnf(c_177,negated_conjecture,
subset(singleton(sK1),singleton(sK2)),
inference(split_conjunct,[status(thm)],[sk_t6_zfmisc_1_neg]) ).
cnf(c_1466,negated_conjecture,
subset(unordered_pair(sK1,sK1),singleton(sK2)),
inference(paramod,[status(thm)],[c_169,c_177]) ).
cnf(c_178,negated_conjecture,
subset(unordered_pair(sK1,sK1),unordered_pair(sK2,sK2)),
inference(paramod,[status(thm)],[c_169,c_1466]) ).
cnf(c_179,negated_conjecture,
sK2 != sK1,
inference(split_conjunct,[status(thm)],[sk_t6_zfmisc_1_neg]) ).
cnf(c_1467,plain,
( singleton(B) = A
| empty_set = A
| ~ subset(A,unordered_pair(B,B)) ),
inference(paramod,[status(thm)],[c_169,c_132]) ).
cnf(c_217,plain,
( unordered_pair(B,B) = A
| empty_set = A
| ~ subset(A,unordered_pair(B,B)) ),
inference(paramod,[status(thm)],[c_169,c_1467]) ).
cnf(c_221,plain,
unordered_pair(A,A) != empty_set,
inference(paramod,[status(thm)],[c_169,c_126]) ).
cnf(c_230,plain,
( empty_set = C
| sK0(C) = B
| sK0(C) = A
| unordered_pair(A,B) != C ),
inference(resolve,[status(thm)],[c_88,c_83]) ).
cnf(c_231,plain,
( empty_set = B
| sK0(B) = A
| unordered_pair(A,A) != B ),
inference(factor,[status(thm)],[c_230]) ).
cnf(c_1468,negated_conjecture,
( unordered_pair(sK2,sK2) = unordered_pair(sK1,sK1)
| empty_set = unordered_pair(sK1,sK1) ),
inference(resolve,[status(thm)],[c_217,c_178]) ).
cnf(c_1469,negated_conjecture,
( unordered_pair(sK2,sK2) = unordered_pair(sK1,sK1)
| unordered_pair(sK1,sK1) = empty_set ),
inference(copy,[status(thm)],[c_1468]) ).
cnf(c_1094,negated_conjecture,
unordered_pair(sK2,sK2) = unordered_pair(sK1,sK1),
inference(resolve,[status(thm)],[c_221,c_1469]) ).
cnf(c_1470,plain,
unordered_pair(A,A) = singleton(A),
inference(copy,[status(thm)],[c_169]) ).
cnf(c_1471,plain,
( empty_set = singleton(A)
| sK0(singleton(A)) = A
| sK0(singleton(A)) = A ),
inference(resolve,[status(thm)],[c_230,c_1470]) ).
cnf(c_1472,plain,
( empty_set = singleton(A)
| sK0(singleton(A)) = A
| sK0(unordered_pair(A,A)) = A ),
inference(paramod,[status(thm)],[c_169,c_1471]) ).
cnf(c_1473,plain,
( empty_set = singleton(A)
| sK0(unordered_pair(A,A)) = A
| sK0(unordered_pair(A,A)) = A ),
inference(paramod,[status(thm)],[c_169,c_1472]) ).
cnf(c_1474,plain,
( empty_set = unordered_pair(A,A)
| sK0(unordered_pair(A,A)) = A
| sK0(unordered_pair(A,A)) = A ),
inference(paramod,[status(thm)],[c_169,c_1473]) ).
cnf(c_1475,plain,
( unordered_pair(A,A) = empty_set
| sK0(unordered_pair(A,A)) = A
| sK0(unordered_pair(A,A)) = A ),
inference(copy,[status(thm)],[c_1474]) ).
cnf(c_1476,plain,
( unordered_pair(A,A) = empty_set
| sK0(unordered_pair(A,A)) = A ),
inference(copy,[status(thm)],[c_1475]) ).
cnf(c_1385,plain,
sK0(unordered_pair(A,A)) = A,
inference(resolve,[status(thm)],[c_221,c_1476]) ).
cnf(c_1477,plain,
( empty_set = unordered_pair(sK1,sK1)
| sK0(unordered_pair(sK1,sK1)) = sK2 ),
inference(resolve,[status(thm)],[c_1094,c_231]) ).
cnf(c_1478,plain,
( empty_set = unordered_pair(sK1,sK1)
| sK1 = sK2 ),
inference(paramod,[status(thm)],[c_1385,c_1477]) ).
cnf(c_1479,plain,
( empty_set = unordered_pair(sK1,sK1)
| sK2 = sK1 ),
inference(copy,[status(thm)],[c_1478]) ).
cnf(c_1480,plain,
( unordered_pair(sK1,sK1) = empty_set
| sK2 = sK1 ),
inference(copy,[status(thm)],[c_1479]) ).
cnf(c_1481,negated_conjecture,
unordered_pair(sK1,sK1) = empty_set,
inference(resolve,[status(thm)],[c_179,c_1480]) ).
cnf(c_1465,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_221,c_1481]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU148+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 08:46:42 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 1401024 was started by sandbox2 on n001,
% 0.16/0.44 % Sat Sep 26 08:46:42 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 1.99/0.78
% 1.99/0.78 % SZS status Theorem for theBenchmark
% 1.99/0.78
% 1.99/0.78 % Proof 1 at 0.23 (+ 0.07) seconds.
% 1.99/0.78 % Length of proof is 21.
% 1.99/0.78 % Level of proof is 4.
% 1.99/0.78 % Maximum clause weight is 16.000.
% 1.99/0.78 % Given clauses 179.
% 1.99/0.78
% 1.99/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------