%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM390+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 : 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 3.69s 0.92s
% Output : Proof 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 132 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 52 ~; 44 |; 26 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 61 ( 0 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f28_nnf,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A,B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B)
| ~ epsilon_transitive(A) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c52,plain,
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f29,conjecture,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( in(B,C)
& subset(A,B) )
=> in(A,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ordinal1) ).
fof(f29_neg,negated_conjecture,
~ ! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( in(B,C)
& subset(A,B) )
=> in(A,C) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(A,C)
& in(B,C)
& subset(A,B)
& ordinal(C) )
& ordinal(B) )
& epsilon_transitive(A) ),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
( ~ in(sk13,sk15)
& in(sk14,sk15)
& subset(sk13,sk14)
& ordinal(sk15)
& ordinal(sk14)
& epsilon_transitive(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14,sk15])],[f29_nnf]) ).
cnf(c53,plain,
epsilon_transitive(sk13),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p116,plain,
( in(sk13,X0)
| ~ proper_subset(sk13,X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
ordinal(sk15),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p122,plain,
( in(sk13,sk15)
| ~ proper_subset(sk13,sk15) ),
inference(resolution,[status(thm)],[p116,c55]) ).
fof(f27,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f27_nnf,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c51,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(c56,plain,
subset(sk13,sk14),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p109,plain,
( subset(sk13,X0)
| ~ subset(sk14,X0) ),
inference(resolution,[status(thm)],[c51,c56]) ).
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(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f3_nnf,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p72,plain,
epsilon_transitive(sk15),
inference(resolution,[status(thm)],[c55,c3]) ).
cnf(p89,plain,
( subset(X0,sk15)
| ~ in(X0,sk15) ),
inference(resolution,[status(thm)],[c10,p72]) ).
cnf(c57,plain,
in(sk14,sk15),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p90,plain,
subset(sk14,sk15),
inference(resolution,[status(thm)],[p89,c57]) ).
cnf(p111,plain,
subset(sk13,sk15),
inference(resolution,[status(thm)],[p109,p90]) ).
fof(f8,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f8_nnf,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c15,plain,
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p112,plain,
( sk13 = sk15
| proper_subset(sk13,sk15) ),
inference(resolution,[status(thm)],[p111,c15]) ).
cnf(p125,plain,
( sk13 = sk15
| in(sk13,sk15) ),
inference(resolution,[status(thm)],[p122,p112]) ).
cnf(c58,plain,
~ in(sk13,sk15),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p132,plain,
sk13 = sk15,
inference(resolution,[status(thm)],[p125,c58]) ).
fof(f36,axiom,
! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(f36_nnf,plain,
! [A,B] :
( ~ subset(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [A,B] :
( ~ subset(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c66,plain,
( ~ subset(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p107,plain,
~ subset(sk15,sk14),
inference(resolution,[status(thm)],[c66,c57]) ).
cnf(p143,plain,
~ subset(sk13,sk14),
inference(superposition,[status(thm)],[p132,p107]) ).
cnf(p155,plain,
$false,
inference(resolution,[status(thm)],[p143,c56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 03:49:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.69/0.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.69/0.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------