%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU161+3 : 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 : 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 08:45:15 AM UTC 2026
% Result : Theorem 0.15s 10.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 20 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 6 ~; 1 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(l23_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(t46_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(t46_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(assume_negation,[status(cth)],[t46_zfmisc_1]) ).
cnf(c_12,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_17,plain,
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(clausify,[status(thm)],[l23_zfmisc_1]) ).
fof(nnf_9,plain,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1_neg]) ).
fof(sk_t46_zfmisc_1_neg,plain,
( set_union2(singleton(sK0),sK1) != sK1
& in(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_9]) ).
cnf(c_18,negated_conjecture,
in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t46_zfmisc_1_neg]) ).
cnf(c_19,negated_conjecture,
set_union2(singleton(sK0),sK1) != sK1,
inference(split_conjunct,[status(thm)],[sk_t46_zfmisc_1_neg]) ).
cnf(c_20,negated_conjecture,
set_union2(sK1,singleton(sK0)) != sK1,
inference(paramod,[status(thm)],[c_12,c_19]) ).
cnf(c_24,negated_conjecture,
set_union2(singleton(sK0),sK1) = sK1,
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_25,negated_conjecture,
set_union2(sK1,singleton(sK0)) = sK1,
inference(paramod,[status(thm)],[c_12,c_24]) ).
cnf(c_23,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_20,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU161+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/10.38 % Computer : n002.cluster.edu
% 0.12/10.38 % Model : x86_64 x86_64
% 0.12/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.38 % Memory : 8046.5625MB
% 0.12/10.38 % OS : Linux 6.8.0-71-generic
% 0.12/10.38 % CPULimit : 300
% 0.12/10.38 % WCLimit : 300
% 0.12/10.38 % DateTime : Sat Sep 26 08:45:32 UTC 2026
% 0.12/10.38 % CPUTime :
% 0.12/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/10.39 % Process 1291488 was started by sandbox on n002,
% 0.12/10.39 % Sat Sep 26 08:45:32 2026
% 0.12/10.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/10.39
% 0.12/10.39 % From the command line: assign(max_seconds, 300).
% 0.15/10.40
% 0.15/10.40 % SZS status Theorem for theBenchmark
% 0.15/10.40
% 0.15/10.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/10.40 % Length of proof is 9.
% 0.15/10.40 % Level of proof is 3.
% 0.15/10.40 % Maximum clause weight is 9.000.
% 0.15/10.40 % Given clauses 9.
% 0.15/10.40
% 0.15/10.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------