%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU362+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:51:51 PM UTC 2026
% Result : Theorem 47.80s 17.47s
% Output : Proof 47.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 23 unt; 0 def)
% Number of atoms : 218 ( 14 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 234 ( 89 ~; 84 |; 34 &)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 103 ( 1 sgn 66 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> rel_str(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
fof(f14_nnf,plain,
! [A] :
( ! [B] :
( rel_str(B)
| ~ subrelstr(B,A) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B] :
( rel_str(B)
| ~ subrelstr(B,A)
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c17,plain,
( rel_str(X1)
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f38,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(B))
=> ( ( related(B,E,F)
& F = D
& E = C )
=> related(A,C,D) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_yellow_0) ).
fof(f38_neg,negated_conjecture,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(B))
=> ( ( related(B,E,F)
& F = D
& E = C )
=> related(A,C,D) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f38_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ~ related(A,C,D)
& related(B,E,F)
& F = D
& E = C
& element(F,the_carrier(B)) )
& element(E,the_carrier(B)) )
& element(D,the_carrier(A)) )
& element(C,the_carrier(A)) )
& subrelstr(B,A) )
& rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f38_neg]) ).
fof(f38_sk,plain,
( ~ related(sk11,sk13,sk14)
& related(sk12,sk15,sk16)
& sk16 = sk14
& sk15 = sk13
& element(sk16,the_carrier(sk12))
& element(sk15,the_carrier(sk12))
& element(sk14,the_carrier(sk11))
& element(sk13,the_carrier(sk11))
& subrelstr(sk12,sk11)
& rel_str(sk11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13,sk14,sk15,sk16])],[f38_nnf]) ).
cnf(c48,plain,
rel_str(sk11),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p96,plain,
( rel_str(X0)
| ~ subrelstr(X0,sk11) ),
inference(resolution,[status(thm)],[c17,c48]) ).
cnf(c49,plain,
subrelstr(sk12,sk11),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p98,plain,
rel_str(sk12),
inference(resolution,[status(thm)],[p96,c49]) ).
fof(f5,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( related(A,B,C)
<=> in(ordered_pair(B,C),the_InternalRel(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f5_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ in(ordered_pair(B,C),the_InternalRel(A))
| related(A,B,C) )
& ( in(ordered_pair(B,C),the_InternalRel(A))
| ~ related(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ( ( ~ in(ordered_pair(B,C),the_InternalRel(A))
| related(A,B,C) )
& ( in(ordered_pair(B,C),the_InternalRel(A))
| ~ related(A,B,C) ) )
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p104,plain,
( in(ordered_pair(X0,X1),the_InternalRel(sk12))
| ~ related(sk12,X0,X1)
| ~ element(X1,the_carrier(sk12))
| ~ element(X0,the_carrier(sk12)) ),
inference(resolution,[status(thm)],[p98,c7]) ).
cnf(c52,plain,
element(sk15,the_carrier(sk12)),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p562,plain,
( in(ordered_pair(sk13,X0),the_InternalRel(sk12))
| ~ related(sk12,sk13,X0)
| ~ element(X0,the_carrier(sk12)) ),
inference(resolution,[status(thm)],[p104,c52]) ).
cnf(c53,plain,
element(sk16,the_carrier(sk12)),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p810,plain,
( in(ordered_pair(sk13,sk14),the_InternalRel(sk12))
| ~ related(sk12,sk13,sk14) ),
inference(resolution,[status(thm)],[p562,c53]) ).
cnf(c54,plain,
sk15 = sk13,
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(c56,plain,
related(sk12,sk15,sk16),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p64,plain,
related(sk12,sk13,sk14),
inference(superposition,[status(thm)],[c54,c56]) ).
cnf(p812,plain,
in(ordered_pair(sk13,sk14),the_InternalRel(sk12)),
inference(resolution,[status(thm)],[p810,p64]) ).
fof(f36,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f36_nnf,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c46,plain,
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p816,plain,
( element(ordered_pair(sk13,sk14),X0)
| ~ element(the_InternalRel(sk12),powerset(X0)) ),
inference(resolution,[status(thm)],[p812,c46]) ).
fof(f35,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f35_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c45,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f4,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( rel_str(B)
=> ( subrelstr(B,A)
<=> ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_0) ).
fof(f4_nnf,plain,
! [A] :
( ! [B] :
( ( ( ~ subset(the_InternalRel(B),the_InternalRel(A))
| ~ subset(the_carrier(B),the_carrier(A))
| subrelstr(B,A) )
& ( ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) )
| ~ subrelstr(B,A) ) )
| ~ rel_str(B) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( ( ~ subset(the_InternalRel(B),the_InternalRel(A))
| ~ subset(the_carrier(B),the_carrier(A))
| subrelstr(B,A) )
& ( ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) )
| ~ subrelstr(B,A) ) )
| ~ rel_str(B)
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p68,plain,
( subset(the_InternalRel(X0),the_InternalRel(sk11))
| ~ subrelstr(X0,sk11)
| ~ rel_str(X0) ),
inference(resolution,[status(thm)],[c5,c48]) ).
cnf(p102,plain,
( subset(the_InternalRel(sk12),the_InternalRel(sk11))
| ~ subrelstr(sk12,sk11) ),
inference(resolution,[status(thm)],[p98,p68]) ).
cnf(p109,plain,
subset(the_InternalRel(sk12),the_InternalRel(sk11)),
inference(resolution,[status(thm)],[p102,c49]) ).
cnf(p330,plain,
element(the_InternalRel(sk12),powerset(the_InternalRel(sk11))),
inference(resolution,[status(thm)],[c45,p109]) ).
cnf(p823,plain,
element(ordered_pair(sk13,sk14),the_InternalRel(sk11)),
inference(resolution,[status(thm)],[p816,p330]) ).
fof(f34,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f34_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c43,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p840,plain,
( in(ordered_pair(sk13,sk14),the_InternalRel(sk11))
| empty(the_InternalRel(sk11)) ),
inference(resolution,[status(thm)],[p823,c43]) ).
cnf(c8,plain,
( ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p86,plain,
( ~ in(ordered_pair(X0,X1),the_InternalRel(sk11))
| related(sk11,X0,X1)
| ~ element(X1,the_carrier(sk11))
| ~ element(X0,the_carrier(sk11)) ),
inference(resolution,[status(thm)],[c8,c48]) ).
cnf(c50,plain,
element(sk13,the_carrier(sk11)),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p90,plain,
( ~ in(ordered_pair(sk13,X0),the_InternalRel(sk11))
| related(sk11,sk13,X0)
| ~ element(X0,the_carrier(sk11)) ),
inference(resolution,[status(thm)],[p86,c50]) ).
cnf(c51,plain,
element(sk14,the_carrier(sk11)),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p483,plain,
( ~ in(ordered_pair(sk13,sk14),the_InternalRel(sk11))
| related(sk11,sk13,sk14) ),
inference(resolution,[status(thm)],[p90,c51]) ).
cnf(p845,plain,
( related(sk11,sk13,sk14)
| empty(the_InternalRel(sk11)) ),
inference(resolution,[status(thm)],[p840,p483]) ).
cnf(c57,plain,
~ related(sk11,sk13,sk14),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p846,plain,
empty(the_InternalRel(sk11)),
inference(resolution,[status(thm)],[p845,c57]) ).
fof(f39,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f39_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c58,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p864,plain,
the_InternalRel(sk11) = empty_set,
inference(resolution,[status(thm)],[p846,c58]) ).
fof(f37,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f37_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c47,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p817,plain,
( ~ empty(X0)
| ~ element(the_InternalRel(sk12),powerset(X0)) ),
inference(resolution,[status(thm)],[p812,c47]) ).
cnf(p821,plain,
~ empty(the_InternalRel(sk11)),
inference(resolution,[status(thm)],[p817,p330]) ).
cnf(p951,plain,
~ empty(empty_set),
inference(demodulation,[status(thm)],[p864,p821]) ).
fof(f25,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f25_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c28,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(p954,plain,
$false,
inference(resolution,[status(thm)],[p951,c28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU362+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/10.38 % Computer : n015.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Thu Sep 24 13:54:06 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 47.80/17.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.80/17.47 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------