%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM405+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 02:19:57 PM UTC 2026
% Result : Theorem 0.16s 10.97s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 55 ( 24 ~; 18 |; 9 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 33 ( 4 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).
fof(f28_nnf,plain,
! [A] :
? [B] :
( ( ordinal(B)
& ~ in(B,A) )
| ( ~ ordinal(B)
& in(B,A) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A] :
( ( ordinal(sk15(A))
& ~ in(sk15(A),A) )
| ( ~ ordinal(sk15(A))
& in(sk15(A),A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15])],[f28_nnf]) ).
cnf(c69,plain,
( ordinal(sk15(X0))
| in(sk15(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f25,axiom,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( ordinal(C)
& in(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).
fof(f25_nnf,plain,
! [A] :
? [B] :
! [C] :
( ( ~ ordinal(C)
| ~ in(C,A)
| in(C,B) )
& ( ( ordinal(C)
& in(C,A) )
| ~ in(C,B) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [C,A] :
( ( ~ ordinal(C)
| ~ in(C,A)
| in(C,sk14(A)) )
& ( ( ordinal(C)
& in(C,A) )
| ~ in(C,sk14(A)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14])],[f25_nnf]) ).
cnf(c64,plain,
( ordinal(X2)
| ~ in(X2,sk14(X0)) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p98,plain,
( ordinal(sk15(sk14(X0)))
| ordinal(sk15(sk14(X0))) ),
inference(resolution,[status(thm)],[c69,c64]) ).
cnf(p118,plain,
ordinal(sk15(sk14(X0))),
inference(factoring,[status(thm)],[p98]) ).
fof(f29,conjecture,
! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_ordinal1) ).
fof(f29_neg,negated_conjecture,
~ ! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
? [A] :
! [B] :
( in(B,A)
| ~ ordinal(B) ),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
! [B] :
( in(B,sk16)
| ~ ordinal(B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f29_nnf]) ).
cnf(c72,plain,
( in(X1,sk16)
| ~ ordinal(X1) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p141,plain,
in(sk15(sk14(X0)),sk16),
inference(resolution,[status(thm)],[p118,c72]) ).
cnf(c65,plain,
( ~ ordinal(X2)
| ~ in(X2,X0)
| in(X2,sk14(X0)) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p159,plain,
( ~ ordinal(sk15(sk14(X0)))
| in(sk15(sk14(X0)),sk14(sk16)) ),
inference(resolution,[status(thm)],[p141,c65]) ).
cnf(p191,plain,
in(sk15(sk14(X0)),sk14(sk16)),
inference(resolution,[status(thm)],[p159,p118]) ).
cnf(c70,plain,
( ~ in(sk15(X0),X0)
| ~ ordinal(sk15(X0)) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p140,plain,
~ in(sk15(sk14(X0)),sk14(X0)),
inference(resolution,[status(thm)],[p118,c70]) ).
cnf(p207,plain,
$false,
inference(resolution,[status(thm)],[p191,p140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.39 % Computer : n009.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Thu Sep 24 03:51:26 UTC 2026
% 0.10/10.40 % CPUTime :
% 0.16/10.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/10.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/10.97 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------