%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU234+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 02:51:26 PM UTC 2026
% Result : Theorem 5.69s 1.41s
% Output : Proof 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 5 unt; 0 def)
% Number of atoms : 154 ( 17 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 161 ( 52 ~; 72 |; 27 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 47 ( 0 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,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(f32_nnf,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [A,B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c77,plain,
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f8,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f8_nnf,plain,
! [A] :
( ( ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) )
| epsilon_connected(A) )
& ( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk2(A),sk1(A))
& sk1(A) != sk2(A)
& ~ in(sk1(A),sk2(A))
& in(sk2(A),A)
& in(sk1(A),A) )
| epsilon_connected(A) )
& ( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A)
| ~ epsilon_connected(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f8_nnf]) ).
cnf(c16,plain,
( in(sk1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f34,conjecture,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f34_neg,negated_conjecture,
~ ! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f34_nnf,plain,
? [A] :
( ~ ordinal(A)
& ! [B] :
( ( subset(B,A)
& ordinal(B) )
| ~ in(B,A) ) ),
inference(nnf_transformation,[status(thm)],[f34_neg]) ).
fof(f34_sk,plain,
! [B] :
( ~ ordinal(sk16)
& ( ( subset(B,sk16)
& ordinal(B) )
| ~ in(B,sk16) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f34_nnf]) ).
cnf(c79,plain,
( ordinal(X1)
| ~ in(X1,sk16) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p132,plain,
( ordinal(sk1(sk16))
| epsilon_connected(sk16) ),
inference(resolution,[status(thm)],[c16,c79]) ).
cnf(p155,plain,
( epsilon_connected(sk16)
| in(X0,sk1(sk16))
| sk1(sk16) = X0
| in(sk1(sk16),X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c77,p132]) ).
cnf(c17,plain,
( in(sk2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p139,plain,
( ordinal(sk2(sk16))
| epsilon_connected(sk16) ),
inference(resolution,[status(thm)],[c17,c79]) ).
cnf(p160,plain,
( epsilon_connected(sk16)
| epsilon_connected(sk16)
| in(sk2(sk16),sk1(sk16))
| sk1(sk16) = sk2(sk16)
| in(sk1(sk16),sk2(sk16)) ),
inference(resolution,[status(thm)],[p155,p139]) ).
cnf(p334,plain,
( epsilon_connected(sk16)
| in(sk2(sk16),sk1(sk16))
| sk1(sk16) = sk2(sk16)
| in(sk1(sk16),sk2(sk16)) ),
inference(factoring,[status(thm)],[p160]) ).
cnf(c20,plain,
( ~ in(sk2(X0),sk1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p558,plain,
( epsilon_connected(sk16)
| epsilon_connected(sk16)
| sk1(sk16) = sk2(sk16)
| in(sk1(sk16),sk2(sk16)) ),
inference(resolution,[status(thm)],[p334,c20]) ).
cnf(p563,plain,
( epsilon_connected(sk16)
| sk1(sk16) = sk2(sk16)
| in(sk1(sk16),sk2(sk16)) ),
inference(factoring,[status(thm)],[p558]) ).
cnf(c18,plain,
( ~ in(sk1(X0),sk2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p564,plain,
( epsilon_connected(sk16)
| epsilon_connected(sk16)
| sk1(sk16) = sk2(sk16) ),
inference(resolution,[status(thm)],[p563,c18]) ).
cnf(p569,plain,
( epsilon_connected(sk16)
| sk1(sk16) = sk2(sk16) ),
inference(factoring,[status(thm)],[p564]) ).
cnf(c19,plain,
( sk1(X0) != sk2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p572,plain,
( epsilon_connected(sk16)
| epsilon_connected(sk16) ),
inference(resolution,[status(thm)],[p569,c19]) ).
cnf(p573,plain,
epsilon_connected(sk16),
inference(factoring,[status(thm)],[p572]) ).
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(c14,plain,
( ~ subset(sk0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c13,plain,
( in(sk0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c80,plain,
( subset(X1,sk16)
| ~ in(X1,sk16) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p112,plain,
( subset(sk0(sk16),sk16)
| epsilon_transitive(sk16) ),
inference(resolution,[status(thm)],[c13,c80]) ).
cnf(p118,plain,
( epsilon_transitive(sk16)
| epsilon_transitive(sk16) ),
inference(resolution,[status(thm)],[c14,p112]) ).
cnf(p119,plain,
epsilon_transitive(sk16),
inference(factoring,[status(thm)],[p118]) ).
fof(f5,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f5_nnf,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c8,plain,
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p120,plain,
( ordinal(sk16)
| ~ epsilon_connected(sk16) ),
inference(resolution,[status(thm)],[p119,c8]) ).
cnf(p574,plain,
ordinal(sk16),
inference(resolution,[status(thm)],[p573,p120]) ).
cnf(c81,plain,
~ ordinal(sk16),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p576,plain,
$false,
inference(resolution,[status(thm)],[p574,c81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU234+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.56 % Computer : n003.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Thu Sep 24 13:21:52 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.69/1.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.69/1.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------