%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU361+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 08:46:05 AM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 125 ( 10 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 140 ( 53 ~; 43 |; 27 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 2 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d11_yellow_0,axiom,
! [A] :
( rel_str(A)
=> bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
file('theBenchmark.p',d11_yellow_0) ).
fof(dt_k1_yellow_0,axiom,
! [A,B] :
( rel_str(A)
=> element(join_on_relstr(A,B),the_carrier(A)) ),
file('theBenchmark.p',dt_k1_yellow_0) ).
fof(t30_yellow_0,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('theBenchmark.p',t30_yellow_0) ).
fof(t42_yellow_0,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('theBenchmark.p',t42_yellow_0) ).
fof(t6_yellow_0,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('theBenchmark.p',t6_yellow_0) ).
fof(t44_yellow_0,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('theBenchmark.p',t44_yellow_0) ).
fof(t44_yellow_0_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(assume_negation,[status(cth)],[t44_yellow_0]) ).
fof(nnf_27,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(fof_nnf,[status(thm)],[t44_yellow_0_neg]) ).
fof(sk_t44_yellow_0_neg,plain,
( ~ related(sK0,bottom_of_relstr(sK0),sK1)
& element(sK1,the_carrier(sK0))
& rel_str(sK0)
& lower_bounded_relstr(sK0)
& antisymmetric_relstr(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_27]) ).
cnf(c_29,negated_conjecture,
rel_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_yellow_0_neg]) ).
cnf(c_30,plain,
( relstr_set_smaller(A,empty_set,B)
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[t6_yellow_0]) ).
cnf(c_32,plain,
( ex_sup_of_relstr_set(A,empty_set)
| ~ rel_str(A)
| ~ lower_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[t42_yellow_0]) ).
cnf(c_39,plain,
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,C)
| join_on_relstr(A,C) != B
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(clausify,[status(thm)],[t30_yellow_0]) ).
cnf(c_44,plain,
( element(join_on_relstr(A,B),the_carrier(A))
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[dt_k1_yellow_0]) ).
cnf(c_45,plain,
( join_on_relstr(A,empty_set) = bottom_of_relstr(A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d11_yellow_0]) ).
cnf(c_55,negated_conjecture,
~ related(sK0,bottom_of_relstr(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_t44_yellow_0_neg]) ).
cnf(c_56,negated_conjecture,
element(sK1,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t44_yellow_0_neg]) ).
cnf(c_57,negated_conjecture,
lower_bounded_relstr(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_yellow_0_neg]) ).
cnf(c_58,negated_conjecture,
antisymmetric_relstr(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_yellow_0_neg]) ).
cnf(c_59,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_yellow_0_neg]) ).
cnf(c_72,negated_conjecture,
( relstr_set_smaller(sK0,empty_set,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_30,c_29]) ).
cnf(c_73,negated_conjecture,
( ex_sup_of_relstr_set(sK0,empty_set)
| ~ lower_bounded_relstr(sK0)
| ~ antisymmetric_relstr(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_32,c_29]) ).
cnf(c_131,negated_conjecture,
( ex_sup_of_relstr_set(sK0,empty_set)
| ~ lower_bounded_relstr(sK0)
| ~ antisymmetric_relstr(sK0) ),
inference(resolve,[status(thm)],[c_59,c_73]) ).
cnf(c_132,negated_conjecture,
( ex_sup_of_relstr_set(sK0,empty_set)
| ~ lower_bounded_relstr(sK0) ),
inference(resolve,[status(thm)],[c_58,c_131]) ).
cnf(c_74,negated_conjecture,
ex_sup_of_relstr_set(sK0,empty_set),
inference(resolve,[status(thm)],[c_57,c_132]) ).
cnf(c_87,negated_conjecture,
( related(sK0,A,C)
| ~ relstr_set_smaller(sK0,B,C)
| ~ element(C,the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,B)
| join_on_relstr(sK0,B) != A
| ~ element(A,the_carrier(sK0))
| ~ antisymmetric_relstr(sK0) ),
inference(resolve,[status(thm)],[c_39,c_29]) ).
cnf(c_88,negated_conjecture,
( related(sK0,A,C)
| ~ relstr_set_smaller(sK0,B,C)
| ~ element(C,the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,B)
| join_on_relstr(sK0,B) != A
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_58,c_87]) ).
cnf(c_104,negated_conjecture,
element(join_on_relstr(sK0,A),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_44,c_29]) ).
cnf(c_107,negated_conjecture,
join_on_relstr(sK0,empty_set) = bottom_of_relstr(sK0),
inference(resolve,[status(thm)],[c_45,c_29]) ).
cnf(c_108,negated_conjecture,
bottom_of_relstr(sK0) = join_on_relstr(sK0,empty_set),
inference(copy,[status(thm)],[c_107]) ).
cnf(c_114,negated_conjecture,
~ related(sK0,join_on_relstr(sK0,empty_set),sK1),
inference(paramod,[status(thm)],[c_108,c_55]) ).
cnf(c_120,plain,
relstr_set_smaller(sK0,empty_set,sK1),
inference(resolve,[status(thm)],[c_72,c_56]) ).
cnf(c_133,negated_conjecture,
( related(sK0,join_on_relstr(sK0,B),C)
| ~ relstr_set_smaller(sK0,A,C)
| ~ element(C,the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,A)
| join_on_relstr(sK0,A) != join_on_relstr(sK0,B) ),
inference(resolve,[status(thm)],[c_88,c_104]) ).
cnf(c_134,plain,
( related(sK0,join_on_relstr(sK0,A),B)
| ~ relstr_set_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,A) ),
inference(xxres,[status(thm)],[c_133]) ).
cnf(c_135,negated_conjecture,
( related(sK0,join_on_relstr(sK0,empty_set),A)
| ~ relstr_set_smaller(sK0,empty_set,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_134,c_74]) ).
cnf(c_136,negated_conjecture,
( related(sK0,join_on_relstr(sK0,empty_set),sK1)
| ~ relstr_set_smaller(sK0,empty_set,sK1) ),
inference(resolve,[status(thm)],[c_135,c_56]) ).
cnf(c_137,negated_conjecture,
~ relstr_set_smaller(sK0,empty_set,sK1),
inference(resolve,[status(thm)],[c_136,c_114]) ).
cnf(c_130,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_120,c_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU361+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 09:18:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2425029 was started by sandbox on n013,
% 0.10/0.38 % Sat Sep 26 09:18:54 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 28.
% 0.10/0.40 % Level of proof is 5.
% 0.10/0.40 % Maximum clause weight is 24.000.
% 0.10/0.40 % Given clauses 48.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------