%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM394+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 : n015.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 4.10s 1.11s
% Output : Proof 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 9 unt; 0 def)
% Number of atoms : 135 ( 10 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 145 ( 53 ~; 61 |; 19 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 47 ( 0 sgn 31 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f27_nnf,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c50,plain,
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f28,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(B,A)
| ordinal_subset(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_ordinal1) ).
fof(f28_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(B,A)
| ordinal_subset(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f28_nnf,plain,
? [A] :
( ? [B] :
( ~ in(B,A)
& ~ ordinal_subset(A,B)
& ordinal(B) )
& ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f28_neg]) ).
fof(f28_sk,plain,
( ~ in(sk14,sk13)
& ~ ordinal_subset(sk13,sk14)
& ordinal(sk14)
& ordinal(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14])],[f28_nnf]) ).
cnf(c52,plain,
ordinal(sk14),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p121,plain,
( in(X0,sk14)
| sk14 = X0
| in(sk14,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c50,c52]) ).
cnf(c51,plain,
ordinal(sk13),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p125,plain,
( in(sk13,sk14)
| sk14 = sk13
| in(sk14,sk13) ),
inference(resolution,[status(thm)],[p121,c51]) ).
cnf(c54,plain,
~ in(sk14,sk13),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p128,plain,
( in(sk13,sk14)
| sk14 = sk13 ),
inference(resolution,[status(thm)],[p125,c54]) ).
fof(f7,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f7_nnf,plain,
! [A] :
( ( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ( ( ~ subset(sk0(A),A)
& in(sk0(A),A) )
| epsilon_transitive(A) )
& ( subset(B,A)
| ~ in(B,A)
| ~ epsilon_transitive(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f7_nnf]) ).
cnf(c10,plain,
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f2,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f2_nnf,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p65,plain,
epsilon_transitive(sk14),
inference(resolution,[status(thm)],[c2,c52]) ).
cnf(p89,plain,
( subset(X0,sk14)
| ~ in(X0,sk14) ),
inference(resolution,[status(thm)],[c10,p65]) ).
cnf(p130,plain,
( subset(sk13,sk14)
| sk14 = sk13 ),
inference(resolution,[status(thm)],[p128,p89]) ).
fof(f23,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(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(c46,plain,
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p110,plain,
( ~ subset(sk13,X0)
| ordinal_subset(sk13,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c46,c51]) ).
cnf(p116,plain,
( ~ subset(sk13,sk14)
| ordinal_subset(sk13,sk14) ),
inference(resolution,[status(thm)],[p110,c52]) ).
cnf(p133,plain,
( ordinal_subset(sk13,sk14)
| sk14 = sk13 ),
inference(resolution,[status(thm)],[p130,p116]) ).
cnf(c53,plain,
~ ordinal_subset(sk13,sk14),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p135,plain,
sk14 = sk13,
inference(resolution,[status(thm)],[p133,c53]) ).
cnf(p136,plain,
~ ordinal_subset(sk13,sk13),
inference(demodulation,[status(thm)],[p135,c53]) ).
fof(f6,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(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(p82,plain,
( ordinal_subset(X0,sk13)
| ordinal_subset(sk13,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c9,c51]) ).
cnf(p91,plain,
( ordinal_subset(sk13,sk13)
| ~ ordinal(sk13) ),
inference(factoring,[status(thm)],[p82]) ).
cnf(p95,plain,
ordinal_subset(sk13,sk13),
inference(resolution,[status(thm)],[p91,c51]) ).
cnf(p140,plain,
$false,
inference(resolution,[status(thm)],[p136,p95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM394+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 03:53:25 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.10/1.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.10/1.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------