%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU230+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:45:30 AM UTC 2026
% Result : Theorem 0.13s 12.05s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 31 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 7 |; 0 &)
% ( 4 <=>; 0 =>; 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 : 28 ( 2 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t10_ordinal1,conjecture,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t10_ordinal1_neg,negated_conjecture,
~ ! [A] : in(A,succ(A)),
inference(assume_negation,[status(cth)],[t10_ordinal1]) ).
cnf(c_50,plain,
succ(A) = set_union2(A,singleton(A)),
inference(clausify,[status(thm)],[d1_ordinal1]) ).
cnf(c_52,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_57,plain,
( ~ in(D,B)
| in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_81,plain,
set_union2(A,empty_set) = A,
inference(clausify,[status(thm)],[t1_boole]) ).
fof(nnf_37,plain,
? [A] : ~ in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1_neg]) ).
fof(sk_t10_ordinal1_neg,plain,
~ in(sK0,succ(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_37]) ).
cnf(c_85,negated_conjecture,
~ in(sK0,succ(sK0)),
inference(split_conjunct,[status(thm)],[sk_t10_ordinal1_neg]) ).
cnf(c_86,negated_conjecture,
~ in(sK0,set_union2(sK0,singleton(sK0))),
inference(paramod,[status(thm)],[c_50,c_85]) ).
cnf(c_96,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_52]) ).
cnf(c_280,plain,
( ~ in(A,C)
| in(A,set_union2(B,C)) ),
inference(xxres,[status(thm)],[c_57]) ).
cnf(c_226,negated_conjecture,
~ in(sK0,singleton(sK0)),
inference(resolve,[status(thm)],[c_280,c_86]) ).
cnf(c_281,plain,
in(set_union2(A,empty_set),singleton(A)),
inference(resolve,[status(thm)],[c_96,c_81]) ).
cnf(c_278,plain,
in(A,singleton(A)),
inference(paramod,[status(thm)],[c_81,c_281]) ).
cnf(c_279,plain,
$false,
inference(resolve,[status(thm)],[c_278,c_226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU230+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/12.01 % Computer : n013.cluster.edu
% 0.08/12.01 % Model : x86_64 x86_64
% 0.08/12.01 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/12.01 % Memory : 8046.5625MB
% 0.08/12.01 % OS : Linux 6.8.0-71-generic
% 0.08/12.01 % CPULimit : 300
% 0.08/12.01 % WCLimit : 300
% 0.08/12.01 % DateTime : Sat Sep 26 08:54:19 UTC 2026
% 0.08/12.01 % CPUTime :
% 0.08/12.01 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/12.01 % Process 2380523 was started by sandbox on n013,
% 0.08/12.01 % Sat Sep 26 08:54:19 2026
% 0.08/12.01 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/12.02
% 0.08/12.02 % From the command line: assign(max_seconds, 300).
% 0.13/12.05
% 0.13/12.05 % SZS status Theorem for theBenchmark
% 0.13/12.05
% 0.13/12.05 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/12.05 % Length of proof is 15.
% 0.13/12.05 % Level of proof is 4.
% 0.13/12.05 % Maximum clause weight is 11.000.
% 0.13/12.05 % Given clauses 47.
% 0.13/12.05
% 0.13/12.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------