%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU149+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:45:11 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% 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_22,negated_conjecture,
singleton(sK0) = unordered_pair(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t8_zfmisc_1_neg]) ).
cnf(c_75,plain,
singleton(sK0) = unordered_pair(sK2,sK1),
inference(paramod,[status(thm)],[c_9,c_22]) ).
cnf(c_106,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_10]) ).
cnf(c_79,negated_conjecture,
~ in(sK1,singleton(sK0)),
inference(resolve,[status(thm)],[c_106,c_23]) ).
cnf(c_107,plain,
( sK1 != B
| unordered_pair(A,B) != singleton(sK0) ),
inference(resolve,[status(thm)],[c_16,c_79]) ).
cnf(c_108,plain,
unordered_pair(A,sK1) != singleton(sK0),
inference(xxres,[status(thm)],[c_107]) ).
cnf(c_104,plain,
singleton(sK0) != unordered_pair(A,sK1),
inference(copy,[status(thm)],[c_108]) ).
cnf(c_105,plain,
$false,
inference(resolve,[status(thm)],[c_104,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU149+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % 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 08:43:21 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1288559 was started by sandbox2 on n002,
% 0.17/0.44 % Sat Sep 26 08:43:21 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 13.
% 0.17/0.46 % Level of proof is 4.
% 0.17/0.46 % Maximum clause weight is 21.000.
% 0.17/0.46 % Given clauses 23.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------