%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM404+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 : n017.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 6.16s 16.43s
% Output : Proof 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 6 unt; 0 def)
% Number of atoms : 204 ( 17 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 215 ( 75 ~; 100 |; 27 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 51 !; 5 ?)
% 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(c81,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)
<=> ordinal(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).
fof(f34_neg,negated_conjecture,
~ ! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f34_nnf,plain,
? [A] :
! [B] :
( ( ~ ordinal(B)
| in(B,A) )
& ( ordinal(B)
| ~ in(B,A) ) ),
inference(nnf_transformation,[status(thm)],[f34_neg]) ).
fof(f34_sk,plain,
! [B] :
( ( ~ ordinal(B)
| in(B,sk18) )
& ( ordinal(B)
| ~ in(B,sk18) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk18])],[f34_nnf]) ).
cnf(c83,plain,
( ordinal(X1)
| ~ in(X1,sk18) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p135,plain,
( ordinal(sk1(sk18))
| epsilon_connected(sk18) ),
inference(resolution,[status(thm)],[c16,c83]) ).
cnf(p254,plain,
( epsilon_connected(sk18)
| in(X0,sk1(sk18))
| sk1(sk18) = X0
| in(sk1(sk18),X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c81,p135]) ).
cnf(c17,plain,
( in(sk2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p141,plain,
( ordinal(sk2(sk18))
| epsilon_connected(sk18) ),
inference(resolution,[status(thm)],[c17,c83]) ).
cnf(p608,plain,
( epsilon_connected(sk18)
| epsilon_connected(sk18)
| in(sk2(sk18),sk1(sk18))
| sk1(sk18) = sk2(sk18)
| in(sk1(sk18),sk2(sk18)) ),
inference(resolution,[status(thm)],[p254,p141]) ).
cnf(p2358,plain,
( epsilon_connected(sk18)
| in(sk2(sk18),sk1(sk18))
| sk1(sk18) = sk2(sk18)
| in(sk1(sk18),sk2(sk18)) ),
inference(factoring,[status(thm)],[p608]) ).
cnf(c20,plain,
( ~ in(sk2(X0),sk1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p3549,plain,
( epsilon_connected(sk18)
| epsilon_connected(sk18)
| sk1(sk18) = sk2(sk18)
| in(sk1(sk18),sk2(sk18)) ),
inference(resolution,[status(thm)],[p2358,c20]) ).
cnf(p3554,plain,
( epsilon_connected(sk18)
| sk1(sk18) = sk2(sk18)
| in(sk1(sk18),sk2(sk18)) ),
inference(factoring,[status(thm)],[p3549]) ).
cnf(c18,plain,
( ~ in(sk1(X0),sk2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p3556,plain,
( epsilon_connected(sk18)
| epsilon_connected(sk18)
| sk1(sk18) = sk2(sk18) ),
inference(resolution,[status(thm)],[p3554,c18]) ).
cnf(p3561,plain,
( epsilon_connected(sk18)
| sk1(sk18) = sk2(sk18) ),
inference(factoring,[status(thm)],[p3556]) ).
cnf(c19,plain,
( sk1(X0) != sk2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p3565,plain,
( epsilon_connected(sk18)
| epsilon_connected(sk18) ),
inference(resolution,[status(thm)],[p3561,c19]) ).
cnf(p3566,plain,
epsilon_connected(sk18),
inference(factoring,[status(thm)],[p3565]) ).
fof(f31,axiom,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f31_nnf,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [B,A] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c80,plain,
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
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(c13,plain,
( in(sk0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p123,plain,
( ordinal(sk0(sk18))
| epsilon_transitive(sk18) ),
inference(resolution,[status(thm)],[c13,c83]) ).
cnf(p238,plain,
( epsilon_transitive(sk18)
| ordinal(X0)
| ~ in(X0,sk0(sk18)) ),
inference(resolution,[status(thm)],[c80,p123]) ).
fof(f9,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk3(A,B),B)
& in(sk3(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f9_nnf]) ).
cnf(c22,plain,
( in(sk3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p245,plain,
( subset(sk0(sk18),X0)
| epsilon_transitive(sk18)
| ordinal(sk3(sk0(sk18),X0)) ),
inference(resolution,[status(thm)],[p238,c22]) ).
cnf(c84,plain,
( ~ ordinal(X1)
| in(X1,sk18) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p269,plain,
( in(sk3(sk0(sk18),X0),sk18)
| subset(sk0(sk18),X0)
| epsilon_transitive(sk18) ),
inference(resolution,[status(thm)],[p245,c84]) ).
cnf(c23,plain,
( ~ in(sk3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p298,plain,
( subset(sk0(sk18),sk18)
| subset(sk0(sk18),sk18)
| epsilon_transitive(sk18) ),
inference(resolution,[status(thm)],[p269,c23]) ).
cnf(p300,plain,
( subset(sk0(sk18),sk18)
| epsilon_transitive(sk18) ),
inference(factoring,[status(thm)],[p298]) ).
cnf(c14,plain,
( ~ subset(sk0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p301,plain,
( epsilon_transitive(sk18)
| epsilon_transitive(sk18) ),
inference(resolution,[status(thm)],[p300,c14]) ).
cnf(p304,plain,
epsilon_transitive(sk18),
inference(factoring,[status(thm)],[p301]) ).
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(p316,plain,
( ordinal(sk18)
| ~ epsilon_connected(sk18) ),
inference(resolution,[status(thm)],[p304,c8]) ).
cnf(p3568,plain,
ordinal(sk18),
inference(resolution,[status(thm)],[p3566,p316]) ).
cnf(p3569,plain,
in(sk18,sk18),
inference(resolution,[status(thm)],[p3568,c84]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p92,plain,
~ in(X0,X0),
inference(factoring,[status(thm)],[c0]) ).
cnf(p3577,plain,
$false,
inference(resolution,[status(thm)],[p3569,p92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/15.39 % Computer : n017.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Thu Sep 24 03:46:46 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.11/15.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.16/16.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.16/16.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------