%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM388+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 : n026.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 2.23s 0.79s
% Output : Proof 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 14 unt; 0 def)
% Number of atoms : 134 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 43 ~; 38 |; 29 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 64 ( 1 sgn 45 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f27_nnf,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c55,plain,
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f23,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(A,B)
& in(C,A) )
=> in(C,B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_ordinal1) ).
fof(f23_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(A,B)
& in(C,A) )
=> in(C,B) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f23_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(C,B)
& in(A,B)
& in(C,A)
& epsilon_transitive(C) )
& ordinal(B) )
& ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f23_neg]) ).
fof(f23_sk,plain,
( ~ in(sk15,sk14)
& in(sk13,sk14)
& in(sk15,sk13)
& epsilon_transitive(sk15)
& ordinal(sk14)
& ordinal(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14,sk15])],[f23_nnf]) ).
cnf(c48,plain,
in(sk15,sk13),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p109,plain,
( element(sk15,X0)
| ~ element(sk13,powerset(X0)) ),
inference(resolution,[status(thm)],[c55,c48]) ).
fof(f26,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f26_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c54,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f6,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f6_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)],[f6]) ).
fof(f6_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])],[f6_nnf]) ).
cnf(c9,plain,
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c46,plain,
ordinal(sk14),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f2,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox2/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(p66,plain,
epsilon_transitive(sk14),
inference(resolution,[status(thm)],[c46,c2]) ).
cnf(p81,plain,
( subset(X0,sk14)
| ~ in(X0,sk14) ),
inference(resolution,[status(thm)],[c9,p66]) ).
cnf(c49,plain,
in(sk13,sk14),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p83,plain,
subset(sk13,sk14),
inference(resolution,[status(thm)],[p81,c49]) ).
cnf(p102,plain,
element(sk13,powerset(sk14)),
inference(resolution,[status(thm)],[c54,p83]) ).
cnf(p113,plain,
element(sk15,sk14),
inference(resolution,[status(thm)],[p109,p102]) ).
fof(f25,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f25_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c52,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p119,plain,
( in(sk15,sk14)
| empty(sk14) ),
inference(resolution,[status(thm)],[p113,c52]) ).
cnf(c50,plain,
~ in(sk15,sk14),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p121,plain,
empty(sk14),
inference(resolution,[status(thm)],[p119,c50]) ).
fof(f29,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f29_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c57,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p124,plain,
sk14 = empty_set,
inference(resolution,[status(thm)],[p121,c57]) ).
fof(f30,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f30_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c58,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p94,plain,
~ empty(sk14),
inference(resolution,[status(thm)],[c58,c49]) ).
cnf(p132,plain,
~ empty(empty_set),
inference(demodulation,[status(thm)],[p124,p94]) ).
fof(f8,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f8_nnf,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c13,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p142,plain,
$false,
inference(resolution,[status(thm)],[p132,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 03:52:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.23/0.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.23/0.79 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------