%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 02:19:56 PM UTC 2026
% Result : Theorem 5.48s 1.20s
% Output : Proof 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 36 ~; 41 |; 12 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f23_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)],[f23]) ).
fof(f23_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)],[f23_nnf]) ).
cnf(c45,plain,
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f29,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> inclusion_comparable(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_ordinal1) ).
fof(f29_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> inclusion_comparable(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
? [A] :
( ? [B] :
( ~ inclusion_comparable(A,B)
& ordinal(B) )
& ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
( ~ inclusion_comparable(sk12,sk13)
& ordinal(sk13)
& ordinal(sk12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13])],[f29_nnf]) ).
cnf(c53,plain,
ordinal(sk13),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p115,plain,
( subset(sk13,X0)
| ~ ordinal_subset(sk13,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c45,c53]) ).
cnf(c52,plain,
ordinal(sk12),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p126,plain,
( subset(sk13,sk12)
| ~ ordinal_subset(sk13,sk12) ),
inference(resolution,[status(thm)],[p115,c52]) ).
fof(f6,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f6_nnf,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c9,plain,
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p108,plain,
( ordinal_subset(X0,sk12)
| ordinal_subset(sk12,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c9,c52]) ).
cnf(p111,plain,
( ordinal_subset(sk13,sk12)
| ordinal_subset(sk12,sk13) ),
inference(resolution,[status(thm)],[p108,c53]) ).
cnf(p128,plain,
( ordinal_subset(sk12,sk13)
| subset(sk13,sk12) ),
inference(resolution,[status(thm)],[p126,p111]) ).
fof(f7,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(B,A)
| subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(f7_nnf,plain,
! [A,B] :
( ( ( ~ subset(B,A)
& ~ subset(A,B) )
| inclusion_comparable(A,B) )
& ( subset(B,A)
| subset(A,B)
| ~ inclusion_comparable(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ( ( ~ subset(B,A)
& ~ subset(A,B) )
| inclusion_comparable(A,B) )
& ( subset(B,A)
| subset(A,B)
| ~ inclusion_comparable(A,B) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c12,plain,
( ~ subset(X1,X0)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p131,plain,
( inclusion_comparable(sk12,sk13)
| ordinal_subset(sk12,sk13) ),
inference(resolution,[status(thm)],[p128,c12]) ).
cnf(c54,plain,
~ inclusion_comparable(sk12,sk13),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p136,plain,
ordinal_subset(sk12,sk13),
inference(resolution,[status(thm)],[p131,c54]) ).
cnf(p114,plain,
( subset(sk12,X0)
| ~ ordinal_subset(sk12,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c45,c52]) ).
cnf(p117,plain,
( subset(sk12,sk13)
| ~ ordinal_subset(sk12,sk13) ),
inference(resolution,[status(thm)],[p114,c53]) ).
cnf(p137,plain,
subset(sk12,sk13),
inference(resolution,[status(thm)],[p136,p117]) ).
cnf(c11,plain,
( ~ subset(X0,X1)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p138,plain,
inclusion_comparable(sk12,sk13),
inference(resolution,[status(thm)],[p137,c11]) ).
cnf(p141,plain,
$false,
inference(resolution,[status(thm)],[p138,c54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 03:50:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.48/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.48/1.20 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------