%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM385+1 : 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 : n003.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 08:16:54 AM UTC 2026
% Result : Theorem 1.42s 0.59s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 23 unt; 0 def)
% Number of atoms : 63 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 21 ~; 15 |; 2 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 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 : 40 ( 1 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
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(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(t10_ordinal1,axiom,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t12_ordinal1,conjecture,
! [A,B] :
( succ(A) = succ(B)
=> A = B ),
file('theBenchmark.p',t12_ordinal1) ).
fof(t12_ordinal1_neg,negated_conjecture,
~ ! [A,B] :
( succ(A) = succ(B)
=> A = B ),
inference(assume_negation,[status(cth)],[t12_ordinal1]) ).
fof(nnf_34,plain,
? [A,B] :
( B != A
& succ(B) = succ(A) ),
inference(fof_nnf,[status(thm)],[t12_ordinal1_neg]) ).
fof(sk_t12_ordinal1_neg,plain,
( sK0 != sK1
& succ(sK0) = succ(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_34]) ).
cnf(c_46,negated_conjecture,
sK0 != sK1,
inference(split_conjunct,[status(thm)],[sk_t12_ordinal1_neg]) ).
cnf(c_47,negated_conjecture,
succ(sK0) = succ(sK1),
inference(split_conjunct,[status(thm)],[sk_t12_ordinal1_neg]) ).
cnf(c_52,plain,
in(A,succ(A)),
inference(clausify,[status(thm)],[t10_ordinal1]) ).
cnf(c_66,plain,
set_union2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
cnf(c_78,plain,
( in(D,B)
| in(D,A)
| ~ in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_82,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_83,plain,
succ(A) = set_union2(A,singleton(A)),
inference(clausify,[status(thm)],[d1_ordinal1]) ).
cnf(c_86,plain,
( ~ in(B,A)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_95,plain,
in(A,set_union2(A,singleton(A))),
inference(paramod,[status(thm)],[c_83,c_52]) ).
cnf(c_605,negated_conjecture,
set_union2(sK0,singleton(sK0)) = succ(sK1),
inference(paramod,[status(thm)],[c_83,c_47]) ).
cnf(c_96,negated_conjecture,
set_union2(sK0,singleton(sK0)) = set_union2(sK1,singleton(sK1)),
inference(paramod,[status(thm)],[c_83,c_605]) ).
cnf(c_606,plain,
A = set_union2(A,A),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_607,plain,
( A = B
| ~ in(A,set_union2(singleton(B),singleton(B))) ),
inference(resolve,[status(thm)],[c_82,c_606]) ).
cnf(c_608,negated_conjecture,
~ in(sK0,set_union2(singleton(sK1),singleton(sK1))),
inference(resolve,[status(thm)],[c_607,c_46]) ).
cnf(c_403,negated_conjecture,
~ in(sK0,singleton(sK1)),
inference(paramod,[status(thm)],[c_66,c_608]) ).
cnf(c_609,plain,
A = set_union2(A,A),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_610,plain,
( A = B
| ~ in(A,set_union2(singleton(B),singleton(B))) ),
inference(resolve,[status(thm)],[c_82,c_609]) ).
cnf(c_611,negated_conjecture,
sK1 != sK0,
inference(copy,[status(thm)],[c_46]) ).
cnf(c_612,negated_conjecture,
~ in(sK1,set_union2(singleton(sK0),singleton(sK0))),
inference(resolve,[status(thm)],[c_610,c_611]) ).
cnf(c_404,negated_conjecture,
~ in(sK1,singleton(sK0)),
inference(paramod,[status(thm)],[c_66,c_612]) ).
cnf(c_613,negated_conjecture,
( in(A,singleton(sK0))
| in(A,sK0)
| ~ in(A,set_union2(sK1,singleton(sK1))) ),
inference(resolve,[status(thm)],[c_78,c_96]) ).
cnf(c_614,negated_conjecture,
( in(sK1,singleton(sK0))
| in(sK1,sK0) ),
inference(resolve,[status(thm)],[c_613,c_95]) ).
cnf(c_502,negated_conjecture,
in(sK1,sK0),
inference(resolve,[status(thm)],[c_404,c_614]) ).
cnf(c_615,negated_conjecture,
set_union2(sK1,singleton(sK1)) = set_union2(sK0,singleton(sK0)),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_616,negated_conjecture,
( in(A,singleton(sK1))
| in(A,sK1)
| ~ in(A,set_union2(sK0,singleton(sK0))) ),
inference(resolve,[status(thm)],[c_78,c_615]) ).
cnf(c_617,negated_conjecture,
( in(sK0,singleton(sK1))
| in(sK0,sK1) ),
inference(resolve,[status(thm)],[c_616,c_95]) ).
cnf(c_525,negated_conjecture,
in(sK0,sK1),
inference(resolve,[status(thm)],[c_403,c_617]) ).
cnf(c_618,plain,
~ in(sK0,sK1),
inference(resolve,[status(thm)],[c_502,c_86]) ).
cnf(c_604,plain,
$false,
inference(resolve,[status(thm)],[c_525,c_618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM385+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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 02:39:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1843693 was started by sandbox on n003,
% 0.09/0.37 % Sat Sep 26 02:39:23 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 1.42/0.59
% 1.42/0.59 % SZS status Theorem for theBenchmark
% 1.42/0.59
% 1.42/0.59 % Proof 1 at 0.13 (+ 0.05) seconds.
% 1.42/0.59 % Length of proof is 22.
% 1.42/0.59 % Level of proof is 4.
% 1.42/0.59 % Maximum clause weight is 24.000.
% 1.42/0.59 % Given clauses 57.
% 1.42/0.59
% 1.42/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------