%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM414+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 : n017.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 08:16:56 AM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 80 ( 15 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 93 ( 42 ~; 28 |; 15 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 23 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(t50_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(B,A)
& A != B
& ~ proper_subset(A,B) ) ) ),
file('theBenchmark.p',t50_ordinal1) ).
fof(t50_ordinal1_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(B,A)
& A != B
& ~ proper_subset(A,B) ) ) ),
inference(assume_negation,[status(cth)],[t50_ordinal1]) ).
cnf(c_74,plain,
( B = A
| ~ subset(A,B)
| proper_subset(A,B) ),
inference(clausify,[status(thm)],[d8_xboole_0]) ).
cnf(c_76,plain,
( subset(A,B)
| ~ ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[redefinition_r1_ordinal1]) ).
cnf(c_91,plain,
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[connectedness_r1_ordinal1]) ).
fof(nnf_41,plain,
? [A] :
( ? [B] :
( ~ proper_subset(B,A)
& B != A
& ~ proper_subset(A,B)
& ordinal(B) )
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[t50_ordinal1_neg]) ).
fof(sk_t50_ordinal1_neg,plain,
( ~ proper_subset(sK1,sK0)
& sK1 != sK0
& ~ proper_subset(sK0,sK1)
& ordinal(sK1)
& ordinal(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_41]) ).
cnf(c_119,negated_conjecture,
ordinal(sK0),
inference(split_conjunct,[status(thm)],[sk_t50_ordinal1_neg]) ).
cnf(c_120,negated_conjecture,
ordinal(sK1),
inference(split_conjunct,[status(thm)],[sk_t50_ordinal1_neg]) ).
cnf(c_121,negated_conjecture,
~ proper_subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t50_ordinal1_neg]) ).
cnf(c_122,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t50_ordinal1_neg]) ).
cnf(c_123,negated_conjecture,
~ proper_subset(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t50_ordinal1_neg]) ).
cnf(c_124,plain,
( B = A
| proper_subset(A,B)
| ~ ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_76,c_74]) ).
cnf(c_211,negated_conjecture,
( A = sK1
| proper_subset(sK1,A)
| ~ ordinal_subset(sK1,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_124,c_120]) ).
cnf(c_212,negated_conjecture,
( sK0 = sK1
| proper_subset(sK1,sK0)
| ~ ordinal_subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_211,c_119]) ).
cnf(c_213,negated_conjecture,
( sK0 = sK1
| ~ ordinal_subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_212,c_123]) ).
cnf(c_214,negated_conjecture,
sK0 != sK1,
inference(copy,[status(thm)],[c_122]) ).
cnf(c_173,negated_conjecture,
~ ordinal_subset(sK1,sK0),
inference(resolve,[status(thm)],[c_213,c_214]) ).
cnf(c_215,negated_conjecture,
( A = sK0
| proper_subset(sK0,A)
| ~ ordinal_subset(sK0,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_124,c_119]) ).
cnf(c_216,negated_conjecture,
( sK1 = sK0
| proper_subset(sK0,sK1)
| ~ ordinal_subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_215,c_120]) ).
cnf(c_217,negated_conjecture,
( sK1 = sK0
| ~ ordinal_subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_216,c_121]) ).
cnf(c_174,negated_conjecture,
~ ordinal_subset(sK0,sK1),
inference(resolve,[status(thm)],[c_217,c_122]) ).
cnf(c_218,negated_conjecture,
( ordinal_subset(sK0,A)
| ordinal_subset(A,sK0)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_91,c_119]) ).
cnf(c_219,negated_conjecture,
( ordinal_subset(sK0,sK1)
| ~ ordinal(sK1) ),
inference(resolve,[status(thm)],[c_218,c_173]) ).
cnf(c_220,negated_conjecture,
~ ordinal(sK1),
inference(resolve,[status(thm)],[c_219,c_174]) ).
cnf(c_210,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_120,c_220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n017.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 02:35:02 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 3810164 was started by sandbox on n017,
% 0.19/0.46 % Sat Sep 26 02:35:02 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 0.19/0.49
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49
% 0.19/0.49 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.19/0.49 % Length of proof is 16.
% 0.19/0.49 % Level of proof is 4.
% 0.19/0.49 % Maximum clause weight is 18.000.
% 0.19/0.49 % Given clauses 65.
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------