%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU361+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 : Thu Sep 24 02:29:07 PM UTC 2026
% Result : Theorem 21.09s 3.25s
% Output : CNFRefutation 21.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 136 ( 10 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 170 ( 65 ~; 57 |; 30 &)
% ( 1 <=>; 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 : 40 ( 1 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t44_yellow_0,conjecture,
! [X1] :
( ( rel_str(X1)
& lower_bounded_relstr(X1)
& antisymmetric_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_yellow_0) ).
fof(t42_yellow_0,lemma,
! [X1] :
( ( rel_str(X1)
& lower_bounded_relstr(X1)
& antisymmetric_relstr(X1)
& ~ empty_carrier(X1) )
=> ( ex_inf_of_relstr_set(X1,the_carrier(X1))
& ex_sup_of_relstr_set(X1,empty_set) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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)
<=> ( ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X4)
=> related(X1,X3,X4) ) )
& relstr_set_smaller(X1,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
fof(t6_yellow_0,lemma,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_element_smaller(X1,empty_set,X2)
& relstr_set_smaller(X1,empty_set,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( rel_str(X1)
& lower_bounded_relstr(X1)
& antisymmetric_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
inference(assume_negation,[status(cth)],[t44_yellow_0]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( rel_str(X1)
& lower_bounded_relstr(X1)
& antisymmetric_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,lemma,
! [X1] :
( ( rel_str(X1)
& lower_bounded_relstr(X1)
& antisymmetric_relstr(X1)
& ~ empty_carrier(X1) )
=> ( ex_inf_of_relstr_set(X1,the_carrier(X1))
& ex_sup_of_relstr_set(X1,empty_set) ) ),
inference(fof_simplification,[status(thm)],[t42_yellow_0]) ).
fof(c_0_9,negated_conjecture,
( ~ related(esk446_0,bottom_of_relstr(esk446_0),esk447_0)
& element(esk447_0,the_carrier(esk446_0))
& rel_str(esk446_0)
& lower_bounded_relstr(esk446_0)
& antisymmetric_relstr(esk446_0)
& ~ empty_carrier(esk446_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_10,plain,
! [X135] :
( bottom_of_relstr(X135) = join_on_relstr(X135,empty_set)
| ~ rel_str(X135) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_yellow_0])])]) ).
fof(c_0_11,plain,
! [X677,X678,X679,X680] :
( ( ~ rel_str(X677)
| ~ element(X679,the_carrier(X677))
| ~ ex_sup_of_relstr_set(X677,X678)
| X679 = join_on_relstr(X677,X678)
| ~ relstr_set_smaller(X677,X678,X679)
| ~ related(X677,X679,esk125_3(X677,X678,X679)) )
& ( ~ rel_str(X677)
| ~ element(X679,the_carrier(X677))
| ~ ex_sup_of_relstr_set(X677,X678)
| X679 = join_on_relstr(X677,X678)
| ~ relstr_set_smaller(X677,X678,X679)
| relstr_set_smaller(X677,X678,esk125_3(X677,X678,X679)) )
& ( ~ rel_str(X677)
| ~ element(X679,the_carrier(X677))
| ~ ex_sup_of_relstr_set(X677,X678)
| X679 = join_on_relstr(X677,X678)
| ~ relstr_set_smaller(X677,X678,X679)
| element(esk125_3(X677,X678,X679),the_carrier(X677)) )
& ( ~ rel_str(X677)
| ~ element(X679,the_carrier(X677))
| ~ ex_sup_of_relstr_set(X677,X678)
| X679 != join_on_relstr(X677,X678)
| related(X677,X679,X680)
| ~ relstr_set_smaller(X677,X678,X680)
| ~ element(X680,the_carrier(X677)) )
& ( ~ rel_str(X677)
| ~ element(X679,the_carrier(X677))
| ~ ex_sup_of_relstr_set(X677,X678)
| X679 != join_on_relstr(X677,X678)
| relstr_set_smaller(X677,X678,X679) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_12,plain,
! [X708,X709] :
( element(join_on_relstr(X708,X709),the_carrier(X708))
| ~ rel_str(X708) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_yellow_0])])]) ).
fof(c_0_13,lemma,
! [X2010] :
( ( ~ rel_str(X2010)
| ~ lower_bounded_relstr(X2010)
| ~ antisymmetric_relstr(X2010)
| empty_carrier(X2010)
| ex_inf_of_relstr_set(X2010,the_carrier(X2010)) )
& ( ~ rel_str(X2010)
| ~ lower_bounded_relstr(X2010)
| ~ antisymmetric_relstr(X2010)
| empty_carrier(X2010)
| ex_sup_of_relstr_set(X2010,empty_set) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_14,negated_conjecture,
~ related(esk446_0,bottom_of_relstr(esk446_0),esk447_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ rel_str(X1)
| bottom_of_relstr(X1) = join_on_relstr(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
rel_str(esk446_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( ~ rel_str(X2)
| ~ element(X4,the_carrier(X2))
| ~ ex_sup_of_relstr_set(X2,X3)
| X4 != join_on_relstr(X2,X3)
| ~ relstr_set_smaller(X2,X3,X1)
| ~ element(X1,the_carrier(X2))
| related(X2,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ rel_str(X1)
| element(join_on_relstr(X1,X2),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,lemma,
( ~ rel_str(X1)
| ~ lower_bounded_relstr(X1)
| ~ antisymmetric_relstr(X1)
| empty_carrier(X1)
| ex_sup_of_relstr_set(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
lower_bounded_relstr(esk446_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
antisymmetric_relstr(esk446_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
~ empty_carrier(esk446_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,negated_conjecture,
~ related(esk446_0,join_on_relstr(esk446_0,empty_set),esk447_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_24,plain,
( ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ ex_sup_of_relstr_set(X1,X2)
| ~ relstr_set_smaller(X1,X2,X3)
| related(X1,join_on_relstr(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18]) ).
cnf(c_0_25,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_19,c_0_20]),c_0_21]),c_0_16])]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
element(esk447_0,the_carrier(esk446_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_27,lemma,
! [X2142,X2143] :
( ( ~ rel_str(X2142)
| ~ element(X2143,the_carrier(X2142))
| relstr_element_smaller(X2142,empty_set,X2143) )
& ( ~ rel_str(X2142)
| ~ element(X2143,the_carrier(X2142))
| relstr_set_smaller(X2142,empty_set,X2143) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_yellow_0])])])])]) ).
cnf(c_0_28,negated_conjecture,
~ relstr_set_smaller(esk446_0,empty_set,esk447_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_16])]) ).
cnf(c_0_29,lemma,
( ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| relstr_set_smaller(X1,empty_set,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU361+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n003.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 : Mon Sep 21 06:17:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.09/3.25 % Version: 3.5.1
% 21.09/3.25 % Preprocessing class: FSLMSMSSSSSNFFN.
% 21.09/3.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 21.09/3.25 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 21.09/3.25 % Starting new_bool_3 with 600s (2) cores
% 21.09/3.25 % Starting new_bool_1 with 600s (2) cores
% 21.09/3.25 % Starting sh5l with 300s (1) cores
% 21.09/3.25 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 3590523 completed with status 0
% 21.09/3.25 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 21.09/3.25 % Preprocessing class: FSLMSMSSSSSNFFN.
% 21.09/3.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 21.09/3.25 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 21.09/3.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 21.09/3.25 % No SInE strategy applied
% 21.09/3.25 % Search class: FGHSM-SMLM32-MFFFFFNN
% 21.09/3.25 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 21.09/3.25 % Starting SubtermCWHack with 82s (1) cores
% 21.09/3.25 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 21.09/3.25 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 21.09/3.25 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 3590541 completed with status 0
% 21.09/3.25 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 21.09/3.25 % Preprocessing class: FSLMSMSSSSSNFFN.
% 21.09/3.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 21.09/3.25 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 21.09/3.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 21.09/3.25 % No SInE strategy applied
% 21.09/3.25 % Search class: FGHSM-SMLM32-MFFFFFNN
% 21.09/3.25 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 21.09/3.25 % Starting SubtermCWHack with 82s (1) cores
% 21.09/3.25 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 21.09/3.25 % Preprocessing time : 0.057 s
% 21.09/3.25 % Presaturation interreduction done
% 21.09/3.25
% 21.09/3.25 % Proof found!
% 21.09/3.25 % SZS status Theorem
% 21.09/3.25 % SZS output start CNFRefutation
% See solution above
% 21.09/3.25 % Parsed axioms : 687
% 21.09/3.25 % Removed by relevancy pruning/SinE : 0
% 21.09/3.25 % Initial clauses : 2911
% 21.09/3.25 % Removed in clause preprocessing : 59
% 21.09/3.25 % Initial clauses in saturation : 2852
% 21.09/3.25 % Processed clauses : 13736
% 21.09/3.25 % ...of these trivial : 108
% 21.09/3.25 % ...subsumed : 6984
% 21.09/3.25 % ...remaining for further processing : 6644
% 21.09/3.25 % Other redundant clauses eliminated : 990
% 21.09/3.25 % Clauses deleted for lack of memory : 0
% 21.09/3.25 % Backward-subsumed : 98
% 21.09/3.25 % Backward-rewritten : 100
% 21.09/3.25 % Generated clauses : 39964
% 21.09/3.25 % ...of the previous two non-redundant : 35871
% 21.09/3.25 % ...aggressively subsumed : 0
% 21.09/3.25 % Contextual simplify-reflections : 327
% 21.09/3.25 % Paramodulations : 39198
% 21.09/3.25 % Factorizations : 2
% 21.09/3.25 % NegExts : 0
% 21.09/3.25 % Equation resolutions : 997
% 21.09/3.25 % Disequality decompositions : 0
% 21.09/3.25 % Total rewrite steps : 8790
% 21.09/3.25 % ...of those cached : 8035
% 21.09/3.25 % Propositional unsat checks : 1
% 21.09/3.25 % Propositional check models : 1
% 21.09/3.25 % Propositional check unsatisfiable : 0
% 21.09/3.25 % Propositional clauses : 0
% 21.09/3.25 % Propositional clauses after purity: 0
% 21.09/3.25 % Propositional unsat core size : 0
% 21.09/3.25 % Propositional preprocessing time : 0.000
% 21.09/3.25 % Propositional encoding time : 0.010
% 21.09/3.25 % Propositional solver time : 0.006
% 21.09/3.25 % Success case prop preproc time : 0.000
% 21.09/3.25 % Success case prop encoding time : 0.000
% 21.09/3.25 % Success case prop solver time : 0.000
% 21.09/3.25 % Current number of processed clauses : 3142
% 21.09/3.25 % Positive orientable unit clauses : 329
% 21.09/3.25 % Positive unorientable unit clauses: 5
% 21.09/3.25 % Negative unit clauses : 580
% 21.09/3.25 % Non-unit-clauses : 2228
% 21.09/3.25 % Current number of unprocessed clauses: 27228
% 21.09/3.25 % ...number of literals in the above : 101795
% 21.09/3.25 % Current number of archived formulas : 0
% 21.09/3.25 % Current number of archived clauses : 2858
% 21.09/3.25 % Clause-clause subsumption calls (NU) : 5180686
% 21.09/3.25 % Rec. Clause-clause subsumption calls : 852782
% 21.09/3.25 % Non-unit clause-clause subsumptions : 3285
% 21.09/3.25 % Unit Clause-clause subsumption calls : 142042
% 21.09/3.25 % Rewrite failures with RHS unbound : 23
% 21.09/3.25 % BW rewrite match attempts : 196
% 21.09/3.25 % BW rewrite match successes : 120
% 21.09/3.25 % Condensation attempts : 0
% 21.09/3.25 % Condensation successes : 0
% 21.09/3.25 % Termbank termtop insertions : 740986
% 21.09/3.25 % Search garbage collected termcells : 40679
% 21.09/3.25
% 21.09/3.25 % -------------------------------------------------
% 21.09/3.25 % User time : 2.605 s
% 21.09/3.25 % System time : 0.053 s
% 21.09/3.25 % Total time : 2.658 s
% 21.09/3.25 % Maximum resident set size: 12012 pages
% 21.09/3.25
% 21.09/3.25 % -------------------------------------------------
% 21.09/3.25 % User time : 7.585 s
% 21.09/3.25 % System time : 0.162 s
% 21.09/3.25 % Total time : 7.748 s
% 21.09/3.25 % Maximum resident set size: 5888 pages
% 21.09/3.25 % E exiting
%------------------------------------------------------------------------------