%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:19:58 PM UTC 2026
% Result : Theorem 4.39s 1.11s
% Output : Proof 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 7 unt; 0 def)
% Number of atoms : 115 ( 22 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 130 ( 51 ~; 50 |; 21 &)
% ( 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 : 33 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f30_nnf,plain,
! [A,B] :
( ( ( ~ subset(A,B)
| ordinal_subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] :
( ( ( ~ subset(A,B)
| ordinal_subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c72,plain,
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f37,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(B,A)
& A != B
& ~ proper_subset(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_ordinal1) ).
fof(f37_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ proper_subset(B,A)
& A != B
& ~ proper_subset(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f37_nnf,plain,
? [A] :
( ? [B] :
( ~ proper_subset(B,A)
& A != B
& ~ proper_subset(A,B)
& ordinal(B) )
& ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f37_neg]) ).
fof(f37_sk,plain,
( ~ proper_subset(sk16,sk15)
& sk15 != sk16
& ~ proper_subset(sk15,sk16)
& ordinal(sk16)
& ordinal(sk15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15,sk16])],[f37_nnf]) ).
cnf(c82,plain,
ordinal(sk16),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p140,plain,
( subset(sk16,X0)
| ~ ordinal_subset(sk16,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c72,c82]) ).
cnf(c81,plain,
ordinal(sk15),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p164,plain,
( subset(sk16,sk15)
| ~ ordinal_subset(sk16,sk15) ),
inference(resolution,[status(thm)],[p140,c81]) ).
fof(f8,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f8_nnf,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c13,plain,
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p113,plain,
( ordinal_subset(X0,sk15)
| ordinal_subset(sk15,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c13,c81]) ).
cnf(p123,plain,
( ordinal_subset(sk16,sk15)
| ordinal_subset(sk15,sk16) ),
inference(resolution,[status(thm)],[p113,c82]) ).
cnf(p169,plain,
( ordinal_subset(sk15,sk16)
| subset(sk16,sk15) ),
inference(resolution,[status(thm)],[p164,p123]) ).
fof(f9,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f9_nnf,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c16,plain,
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p174,plain,
( sk16 = sk15
| proper_subset(sk16,sk15)
| ordinal_subset(sk15,sk16) ),
inference(resolution,[status(thm)],[p169,c16]) ).
cnf(p137,plain,
( subset(sk15,X0)
| ~ ordinal_subset(sk15,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c72,c81]) ).
cnf(p145,plain,
( subset(sk15,sk16)
| ~ ordinal_subset(sk15,sk16) ),
inference(resolution,[status(thm)],[p137,c82]) ).
cnf(p213,plain,
( subset(sk15,sk16)
| sk16 = sk15
| proper_subset(sk16,sk15) ),
inference(resolution,[status(thm)],[p174,p145]) ).
cnf(p215,plain,
( sk15 = sk16
| proper_subset(sk15,sk16)
| sk16 = sk15
| proper_subset(sk16,sk15) ),
inference(resolution,[status(thm)],[p213,c16]) ).
cnf(c85,plain,
~ proper_subset(sk16,sk15),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p239,plain,
( sk15 = sk16
| proper_subset(sk15,sk16)
| sk16 = sk15 ),
inference(resolution,[status(thm)],[p215,c85]) ).
cnf(c83,plain,
~ proper_subset(sk15,sk16),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p240,plain,
( sk15 = sk16
| sk16 = sk15 ),
inference(resolution,[status(thm)],[p239,c83]) ).
cnf(c84,plain,
sk15 != sk16,
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p241,plain,
( sk15 != sk15
| sk15 = sk16 ),
inference(superposition,[status(thm)],[p240,c84]) ).
cnf(p270,plain,
sk15 = sk16,
inference(equality_resolution,[status(thm)],[p241]) ).
cnf(p274,plain,
$false,
inference(resolution,[status(thm)],[p270,c84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM414+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 03:51:21 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.39/1.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.39/1.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------