%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM387+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 : n001.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 14 unt; 0 def)
% Number of atoms : 18 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 7 ~; 1 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 6 !; 1 ?)
% 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(t10_ordinal1,axiom,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t14_ordinal1,conjecture,
! [A] : A != succ(A),
file('theBenchmark.p',t14_ordinal1) ).
fof(t14_ordinal1_neg,negated_conjecture,
~ ! [A] : A != succ(A),
inference(assume_negation,[status(cth)],[t14_ordinal1]) ).
fof(nnf_32,plain,
? [A] : succ(A) = A,
inference(fof_nnf,[status(thm)],[t14_ordinal1_neg]) ).
fof(sk_t14_ordinal1_neg,plain,
succ(sK0) = sK0,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_32]) ).
cnf(c_44,negated_conjecture,
succ(sK0) = sK0,
inference(split_conjunct,[status(thm)],[sk_t14_ordinal1_neg]) ).
cnf(c_49,plain,
in(A,succ(A)),
inference(clausify,[status(thm)],[t10_ordinal1]) ).
cnf(c_70,plain,
succ(A) = set_union2(A,singleton(A)),
inference(clausify,[status(thm)],[d1_ordinal1]) ).
cnf(c_73,plain,
( ~ in(B,A)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_75,plain,
in(A,set_union2(A,singleton(A))),
inference(paramod,[status(thm)],[c_70,c_49]) ).
cnf(c_76,negated_conjecture,
set_union2(sK0,singleton(sK0)) = sK0,
inference(paramod,[status(thm)],[c_70,c_44]) ).
cnf(c_77,plain,
~ in(A,A),
inference(factor,[status(thm)],[c_73]) ).
cnf(c_107,plain,
in(sK0,sK0),
inference(paramod,[status(thm)],[c_76,c_75]) ).
cnf(c_106,plain,
$false,
inference(resolve,[status(thm)],[c_77,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM387+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 02:43:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 730187 was started by sandbox on n001,
% 0.08/0.35 % Sat Sep 26 02:43:56 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 12.
% 0.13/0.38 % Level of proof is 3.
% 0.13/0.38 % Maximum clause weight is 7.000.
% 0.13/0.38 % Given clauses 30.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------