%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU361+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:12:04 PM UTC 2026
% Result : Theorem 11.32s 7.14s
% Output : CNFRefutation 11.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 131 ( 11 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 162 ( 62 ~; 57 |; 27 &)
% ( 1 <=>; 15 =>; 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 : 38 ( 1 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t44_yellow_0,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_yellow_0) ).
fof(t42_yellow_0,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_0) ).
fof(d11_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> bottom_of_relstr(X1) = join_on_relstr(X1,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_yellow_0) ).
fof(d9_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( ex_sup_of_relstr_set(X1,X2)
=> ( X3 = join_on_relstr(X1,X2)
<=> ( relstr_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X4)
=> related(X1,X3,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_yellow_0) ).
fof(dt_k1_yellow_0,axiom,
! [X1,X2] :
( rel_str(X1)
=> element(join_on_relstr(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
fof(t6_yellow_0,lemma,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t44_yellow_0])]) ).
fof(c_0_7,lemma,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[t42_yellow_0]) ).
fof(c_0_8,plain,
! [X1970] :
( ~ rel_str(X1970)
| bottom_of_relstr(X1970) = join_on_relstr(X1970,empty_set) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_yellow_0])]) ).
fof(c_0_9,negated_conjecture,
( ~ empty_carrier(esk446_0)
& antisymmetric_relstr(esk446_0)
& lower_bounded_relstr(esk446_0)
& rel_str(esk446_0)
& element(esk447_0,the_carrier(esk446_0))
& ~ related(esk446_0,bottom_of_relstr(esk446_0),esk447_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X2512,X2513,X2514,X2515] :
( ( relstr_set_smaller(X2512,X2513,X2514)
| X2514 != join_on_relstr(X2512,X2513)
| ~ ex_sup_of_relstr_set(X2512,X2513)
| ~ element(X2514,the_carrier(X2512))
| ~ rel_str(X2512) )
& ( ~ element(X2515,the_carrier(X2512))
| ~ relstr_set_smaller(X2512,X2513,X2515)
| related(X2512,X2514,X2515)
| X2514 != join_on_relstr(X2512,X2513)
| ~ ex_sup_of_relstr_set(X2512,X2513)
| ~ element(X2514,the_carrier(X2512))
| ~ rel_str(X2512) )
& ( element(esk125_3(X2512,X2513,X2514),the_carrier(X2512))
| ~ relstr_set_smaller(X2512,X2513,X2514)
| X2514 = join_on_relstr(X2512,X2513)
| ~ ex_sup_of_relstr_set(X2512,X2513)
| ~ element(X2514,the_carrier(X2512))
| ~ rel_str(X2512) )
& ( relstr_set_smaller(X2512,X2513,esk125_3(X2512,X2513,X2514))
| ~ relstr_set_smaller(X2512,X2513,X2514)
| X2514 = join_on_relstr(X2512,X2513)
| ~ ex_sup_of_relstr_set(X2512,X2513)
| ~ element(X2514,the_carrier(X2512))
| ~ rel_str(X2512) )
& ( ~ related(X2512,X2514,esk125_3(X2512,X2513,X2514))
| ~ relstr_set_smaller(X2512,X2513,X2514)
| X2514 = join_on_relstr(X2512,X2513)
| ~ ex_sup_of_relstr_set(X2512,X2513)
| ~ element(X2514,the_carrier(X2512))
| ~ rel_str(X2512) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_yellow_0])])])])]) ).
fof(c_0_11,plain,
! [X2543,X2544] :
( ~ rel_str(X2543)
| element(join_on_relstr(X2543,X2544),the_carrier(X2543)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_yellow_0])]) ).
fof(c_0_12,lemma,
! [X3977,X3978] :
( ( relstr_set_smaller(X3977,empty_set,X3978)
| ~ element(X3978,the_carrier(X3977))
| ~ rel_str(X3977) )
& ( relstr_element_smaller(X3977,empty_set,X3978)
| ~ element(X3978,the_carrier(X3977))
| ~ rel_str(X3977) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_yellow_0])])])]) ).
fof(c_0_13,lemma,
! [X3845] :
( ( ex_sup_of_relstr_set(X3845,empty_set)
| empty_carrier(X3845)
| ~ antisymmetric_relstr(X3845)
| ~ lower_bounded_relstr(X3845)
| ~ rel_str(X3845) )
& ( ex_inf_of_relstr_set(X3845,the_carrier(X3845))
| empty_carrier(X3845)
| ~ antisymmetric_relstr(X3845)
| ~ lower_bounded_relstr(X3845)
| ~ rel_str(X3845) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_14,plain,
( bottom_of_relstr(X1) = join_on_relstr(X1,empty_set)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
rel_str(esk446_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( related(X2,X4,X1)
| ~ element(X1,the_carrier(X2))
| ~ relstr_set_smaller(X2,X3,X1)
| X4 != join_on_relstr(X2,X3)
| ~ ex_sup_of_relstr_set(X2,X3)
| ~ element(X4,the_carrier(X2))
| ~ rel_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( element(join_on_relstr(X1,X2),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,lemma,
( relstr_set_smaller(X1,empty_set,X2)
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
element(esk447_0,the_carrier(esk446_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,lemma,
( ex_sup_of_relstr_set(X1,empty_set)
| empty_carrier(X1)
| ~ antisymmetric_relstr(X1)
| ~ lower_bounded_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
antisymmetric_relstr(esk446_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
lower_bounded_relstr(esk446_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,negated_conjecture,
~ empty_carrier(esk446_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
~ related(esk446_0,bottom_of_relstr(esk446_0),esk447_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
bottom_of_relstr(esk446_0) = join_on_relstr(esk446_0,empty_set),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_26,plain,
( related(X1,join_on_relstr(X1,X2),X3)
| ~ relstr_set_smaller(X1,X2,X3)
| ~ ex_sup_of_relstr_set(X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).
cnf(c_0_27,negated_conjecture,
relstr_set_smaller(esk446_0,empty_set,esk447_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15])]) ).
cnf(c_0_28,negated_conjecture,
ex_sup_of_relstr_set(esk446_0,empty_set),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_15])]),c_0_23]) ).
cnf(c_0_29,negated_conjecture,
~ related(esk446_0,join_on_relstr(esk446_0,empty_set),esk447_0),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_19]),c_0_15])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU361+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 03:01:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 11.32/7.14 % Version : CSE_E---1.7
% 11.32/7.14 % Problem : theBenchmark.p
% 11.32/7.14 % SZS status Theorem for theBenchmark.p
% 11.32/7.14 % SZS output start CNFRefutation
% See solution above
% 11.32/7.17 % Total time : 5.592s
%------------------------------------------------------------------------------