%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET874+1 : 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 : n013.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 08:37:12 AM UTC 2026
% Result : Theorem 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 8 unt; 0 def)
% Number of atoms : 21 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 5 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 3 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(l23_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(t14_zfmisc_1,conjecture,
! [A,B] : set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B),
file('theBenchmark.p',t14_zfmisc_1) ).
fof(t14_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] : set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B),
inference(assume_negation,[status(cth)],[t14_zfmisc_1]) ).
cnf(c_16,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_24,plain,
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(clausify,[status(thm)],[l23_zfmisc_1]) ).
fof(nnf_11,plain,
? [A,B] : set_union2(singleton(A),unordered_pair(A,B)) != unordered_pair(A,B),
inference(fof_nnf,[status(thm)],[t14_zfmisc_1_neg]) ).
fof(sk_t14_zfmisc_1_neg,plain,
set_union2(singleton(sK0),unordered_pair(sK0,sK1)) != unordered_pair(sK0,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_11]) ).
cnf(c_27,negated_conjecture,
set_union2(singleton(sK0),unordered_pair(sK0,sK1)) != unordered_pair(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t14_zfmisc_1_neg]) ).
cnf(c_34,plain,
( A != B
| in(A,unordered_pair(B,C)) ),
inference(xxres,[status(thm)],[c_16]) ).
cnf(c_66,negated_conjecture,
~ in(sK0,unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_24,c_27]) ).
cnf(c_95,plain,
in(A,unordered_pair(A,B)),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_96,plain,
$false,
inference(resolve,[status(thm)],[c_95,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET874+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:23:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2322263 was started by sandbox2 on n013,
% 0.10/0.37 % Sat Sep 26 08:23:22 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.38
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38
% 0.15/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.38 % Length of proof is 10.
% 0.15/0.38 % Level of proof is 4.
% 0.15/0.38 % Maximum clause weight is 25.000.
% 0.15/0.38 % Given clauses 21.
% 0.15/0.38
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------