%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU361+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 : n007.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 02:51:50 PM UTC 2026
% Result : Theorem 4.17s 1.09s
% Output : Proof 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 12 unt; 0 def)
% Number of atoms : 185 ( 15 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 219 ( 81 ~; 80 |; 41 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 60 ( 2 sgn 35 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) )
=> ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) ) )
& ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
=> ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_yellow_0) ).
fof(f21_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
| ? [D] :
( ~ related(A,B,D)
& relstr_set_smaller(A,C,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,C,B) )
& ( ( ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) ) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D] :
( ( ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
| ( ~ related(A,B,sk7(A,B,C))
& relstr_set_smaller(A,C,sk7(A,B,C))
& element(sk7(A,B,C),the_carrier(A)) )
| ~ relstr_set_smaller(A,C,B) )
& ( ( ( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) ) )
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f21_nnf]) ).
cnf(c24,plain,
( related(X0,X1,X3)
| ~ relstr_set_smaller(X0,X2,X3)
| ~ element(X3,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X2)
| X1 != join_on_relstr(X0,X2)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f23,conjecture,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> related(A,bottom_of_relstr(A),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_yellow_0) ).
fof(f23_neg,negated_conjecture,
~ ! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> related(A,bottom_of_relstr(A),B) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f23_nnf,plain,
? [A] :
( ? [B] :
( ~ related(A,bottom_of_relstr(A),B)
& element(B,the_carrier(A)) )
& rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f23_neg]) ).
fof(f23_sk,plain,
( ~ related(sk8,bottom_of_relstr(sk8),sk9)
& element(sk9,the_carrier(sk8))
& rel_str(sk8)
& lower_bounded_relstr(sk8)
& antisymmetric_relstr(sk8)
& ~ empty_carrier(sk8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f23_nnf]) ).
cnf(c34,plain,
antisymmetric_relstr(sk8),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p80,plain,
( related(sk8,X0,X2)
| ~ relstr_set_smaller(sk8,X1,X2)
| ~ element(X2,the_carrier(sk8))
| ~ ex_sup_of_relstr_set(sk8,X1)
| X0 != join_on_relstr(sk8,X1)
| ~ element(X0,the_carrier(sk8))
| ~ rel_str(sk8) ),
inference(resolution,[status(thm)],[c24,c34]) ).
cnf(c36,plain,
rel_str(sk8),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p193,plain,
( related(sk8,X0,X2)
| ~ relstr_set_smaller(sk8,X1,X2)
| ~ element(X2,the_carrier(sk8))
| ~ ex_sup_of_relstr_set(sk8,X1)
| X0 != join_on_relstr(sk8,X1)
| ~ element(X0,the_carrier(sk8)) ),
inference(resolution,[status(thm)],[p80,c36]) ).
fof(f2,axiom,
! [A] :
( rel_str(A)
=> bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).
fof(f2_nnf,plain,
! [A] :
( bottom_of_relstr(A) = join_on_relstr(A,empty_set)
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] :
( bottom_of_relstr(A) = join_on_relstr(A,empty_set)
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( bottom_of_relstr(X0) = join_on_relstr(X0,empty_set)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p45,plain,
bottom_of_relstr(sk8) = join_on_relstr(sk8,empty_set),
inference(resolution,[status(thm)],[c2,c36]) ).
fof(f4,axiom,
! [A,B] :
( rel_str(A)
=> element(join_on_relstr(A,B),the_carrier(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
fof(f4_nnf,plain,
! [A,B] :
( element(join_on_relstr(A,B),the_carrier(A))
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( element(join_on_relstr(A,B),the_carrier(A))
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p48,plain,
element(join_on_relstr(sk8,X0),the_carrier(sk8)),
inference(resolution,[status(thm)],[c4,c36]) ).
cnf(p50,plain,
element(bottom_of_relstr(sk8),the_carrier(sk8)),
inference(superposition,[status(thm)],[p45,p48]) ).
cnf(p384,plain,
( related(sk8,bottom_of_relstr(sk8),X1)
| ~ relstr_set_smaller(sk8,X0,X1)
| ~ element(X1,the_carrier(sk8))
| ~ ex_sup_of_relstr_set(sk8,X0)
| bottom_of_relstr(sk8) != join_on_relstr(sk8,X0) ),
inference(resolution,[status(thm)],[p193,p50]) ).
cnf(p398,plain,
( related(sk8,bottom_of_relstr(sk8),X0)
| ~ relstr_set_smaller(sk8,empty_set,X0)
| ~ element(X0,the_carrier(sk8))
| ~ ex_sup_of_relstr_set(sk8,empty_set) ),
inference(resolution,[status(thm)],[p384,p45]) ).
fof(f22,axiom,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).
fof(f22_nnf,plain,
! [A] :
( ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) )
| ~ rel_str(A)
| ~ lower_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A] :
( ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) )
| ~ rel_str(A)
| ~ lower_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| empty_carrier(A) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c31,plain,
( ex_sup_of_relstr_set(X0,empty_set)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p111,plain,
( ex_sup_of_relstr_set(sk8,empty_set)
| ~ rel_str(sk8)
| ~ lower_bounded_relstr(sk8)
| empty_carrier(sk8) ),
inference(resolution,[status(thm)],[c31,c34]) ).
cnf(c35,plain,
lower_bounded_relstr(sk8),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p112,plain,
( ex_sup_of_relstr_set(sk8,empty_set)
| ~ rel_str(sk8)
| empty_carrier(sk8) ),
inference(resolution,[status(thm)],[p111,c35]) ).
cnf(p113,plain,
( ex_sup_of_relstr_set(sk8,empty_set)
| empty_carrier(sk8) ),
inference(resolution,[status(thm)],[p112,c36]) ).
cnf(p399,plain,
( empty_carrier(sk8)
| related(sk8,bottom_of_relstr(sk8),X0)
| ~ relstr_set_smaller(sk8,empty_set,X0)
| ~ element(X0,the_carrier(sk8)) ),
inference(resolution,[status(thm)],[p398,p113]) ).
cnf(c37,plain,
element(sk9,the_carrier(sk8)),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p400,plain,
( empty_carrier(sk8)
| related(sk8,bottom_of_relstr(sk8),sk9)
| ~ relstr_set_smaller(sk8,empty_set,sk9) ),
inference(resolution,[status(thm)],[p399,c37]) ).
fof(f25,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f25_nnf,plain,
! [A] :
( ! [B] :
( ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B] :
( ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) )
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c40,plain,
( relstr_set_smaller(X0,empty_set,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p119,plain,
( relstr_set_smaller(sk8,empty_set,X0)
| ~ element(X0,the_carrier(sk8)) ),
inference(resolution,[status(thm)],[c40,c36]) ).
cnf(p121,plain,
relstr_set_smaller(sk8,empty_set,sk9),
inference(resolution,[status(thm)],[p119,c37]) ).
cnf(p406,plain,
( empty_carrier(sk8)
| related(sk8,bottom_of_relstr(sk8),sk9) ),
inference(resolution,[status(thm)],[p400,p121]) ).
cnf(c38,plain,
~ related(sk8,bottom_of_relstr(sk8),sk9),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p407,plain,
empty_carrier(sk8),
inference(resolution,[status(thm)],[p406,c38]) ).
cnf(c33,plain,
~ empty_carrier(sk8),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p408,plain,
$false,
inference(resolution,[status(thm)],[p407,c33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU361+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 13:48:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.17/1.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.17/1.09 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------