%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET904+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 : n012.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 08:37:15 AM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 20 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 1 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 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(l21_zfmisc_1,axiom,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('theBenchmark.p',l21_zfmisc_1) ).
fof(t45_zfmisc_1,conjecture,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('theBenchmark.p',t45_zfmisc_1) ).
fof(t45_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
inference(assume_negation,[status(cth)],[t45_zfmisc_1]) ).
cnf(c_13,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_19,plain,
( in(A,B)
| ~ subset(set_union2(singleton(A),B),B) ),
inference(clausify,[status(thm)],[l21_zfmisc_1]) ).
fof(nnf_10,plain,
? [A,B] :
( ~ in(A,B)
& subset(set_union2(singleton(A),B),B) ),
inference(fof_nnf,[status(thm)],[t45_zfmisc_1_neg]) ).
fof(sk_t45_zfmisc_1_neg,plain,
( ~ in(sK0,sK1)
& subset(set_union2(singleton(sK0),sK1),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_10]) ).
cnf(c_20,negated_conjecture,
subset(set_union2(singleton(sK0),sK1),sK1),
inference(split_conjunct,[status(thm)],[sk_t45_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
subset(set_union2(sK1,singleton(sK0)),sK1),
inference(paramod,[status(thm)],[c_13,c_20]) ).
cnf(c_22,negated_conjecture,
~ in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t45_zfmisc_1_neg]) ).
cnf(c_28,negated_conjecture,
~ subset(set_union2(singleton(sK0),sK1),sK1),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_29,negated_conjecture,
~ subset(set_union2(sK1,singleton(sK0)),sK1),
inference(paramod,[status(thm)],[c_13,c_28]) ).
cnf(c_27,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_21,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET904+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n012.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:24:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 131349 was started by sandbox2 on n012,
% 0.09/0.36 % Sat Sep 26 08:24:36 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 9.
% 0.09/0.38 % Level of proof is 3.
% 0.09/0.38 % Maximum clause weight is 9.000.
% 0.09/0.38 % Given clauses 11.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------