%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU149+1 : 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 : 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 08:45:11 AM UTC 2026
% Result : Theorem 0.10s 5.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 34 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 7 |; 2 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 33 ( 4 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
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(t8_zfmisc_1,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t8_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
inference(assume_negation,[status(cth)],[t8_zfmisc_1]) ).
cnf(c_9,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_10,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_16,plain,
( D != B
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
fof(nnf_7,plain,
? [A,B,C] :
( B != A
& singleton(A) = unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1_neg]) ).
fof(sk_t8_zfmisc_1_neg,plain,
( sK1 != sK0
& singleton(sK0) = unordered_pair(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_7]) ).
cnf(c_20,negated_conjecture,
singleton(sK0) = unordered_pair(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t8_zfmisc_1_neg]) ).
cnf(c_73,plain,
singleton(sK0) = unordered_pair(sK2,sK1),
inference(paramod,[status(thm)],[c_9,c_20]) ).
cnf(c_104,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_10]) ).
cnf(c_77,negated_conjecture,
~ in(sK1,singleton(sK0)),
inference(resolve,[status(thm)],[c_104,c_21]) ).
cnf(c_105,plain,
( sK1 != B
| unordered_pair(A,B) != singleton(sK0) ),
inference(resolve,[status(thm)],[c_16,c_77]) ).
cnf(c_106,plain,
unordered_pair(A,sK1) != singleton(sK0),
inference(xxres,[status(thm)],[c_105]) ).
cnf(c_102,plain,
singleton(sK0) != unordered_pair(A,sK1),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_103,plain,
$false,
inference(resolve,[status(thm)],[c_102,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU149+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 08:40:57 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 1270706 was started by sandbox2 on n004,
% 0.10/5.38 % Sat Sep 26 08:40:57 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.10/5.40
% 0.10/5.40 % SZS status Theorem for theBenchmark
% 0.10/5.40
% 0.10/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/5.40 % Length of proof is 13.
% 0.10/5.40 % Level of proof is 4.
% 0.10/5.40 % Maximum clause weight is 21.000.
% 0.10/5.40 % Given clauses 21.
% 0.10/5.40
% 0.10/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------