%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU355+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:24:50 PM UTC 2026
% Result : Theorem 46.21s 7.25s
% Output : CNFRefutation 46.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 90 ( 5 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 109 ( 41 ~; 41 |; 11 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 2 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t6_yellow_0,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(d8_lattice3,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
fof(d9_lattice3,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X4,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
fof(c_0_4,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_element_smaller(X1,empty_set,X2)
& relstr_set_smaller(X1,empty_set,X2) ) ) ),
inference(assume_negation,[status(cth)],[t6_yellow_0]) ).
fof(c_0_6,plain,
! [X34,X35,X36] :
( ( X36 = empty_set
| in(esk4_1(X36),X36) )
& ( ~ in(X35,X34)
| X34 != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
fof(c_0_7,plain,
! [X23,X24,X25,X26] :
( ( ~ rel_str(X23)
| ~ element(X25,the_carrier(X23))
| relstr_element_smaller(X23,X24,X25)
| ~ related(X23,X25,esk3_3(X23,X24,X25)) )
& ( ~ rel_str(X23)
| ~ element(X25,the_carrier(X23))
| relstr_element_smaller(X23,X24,X25)
| in(esk3_3(X23,X24,X25),X24) )
& ( ~ rel_str(X23)
| ~ element(X25,the_carrier(X23))
| relstr_element_smaller(X23,X24,X25)
| element(esk3_3(X23,X24,X25),the_carrier(X23)) )
& ( ~ rel_str(X23)
| ~ element(X25,the_carrier(X23))
| related(X23,X25,X26)
| ~ in(X26,X24)
| ~ element(X26,the_carrier(X23))
| ~ relstr_element_smaller(X23,X24,X25) ) ),
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)],[d8_lattice3])])])])])]) ).
fof(c_0_8,negated_conjecture,
( ( ~ relstr_element_smaller(esk1_0,empty_set,esk2_0)
| ~ relstr_set_smaller(esk1_0,empty_set,esk2_0) )
& element(esk2_0,the_carrier(esk1_0))
& rel_str(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_9,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| relstr_element_smaller(X1,X2,X3)
| in(esk3_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
element(esk2_0,the_carrier(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
rel_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X46,X47,X48,X49] :
( ( ~ rel_str(X46)
| ~ element(X48,the_carrier(X46))
| relstr_set_smaller(X46,X47,X48)
| ~ related(X46,esk7_3(X46,X47,X48),X48) )
& ( ~ rel_str(X46)
| ~ element(X48,the_carrier(X46))
| relstr_set_smaller(X46,X47,X48)
| in(esk7_3(X46,X47,X48),X47) )
& ( ~ rel_str(X46)
| ~ element(X48,the_carrier(X46))
| relstr_set_smaller(X46,X47,X48)
| element(esk7_3(X46,X47,X48),the_carrier(X46)) )
& ( ~ rel_str(X46)
| ~ element(X48,the_carrier(X46))
| related(X46,X49,X48)
| ~ in(X49,X47)
| ~ element(X49,the_carrier(X46))
| ~ relstr_set_smaller(X46,X47,X48) ) ),
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_lattice3])])])])])]) ).
cnf(c_0_14,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( in(esk3_3(esk1_0,X1,esk2_0),X1)
| relstr_element_smaller(esk1_0,X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_16,plain,
( ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| relstr_set_smaller(X1,X2,X3)
| in(esk7_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( ~ relstr_element_smaller(esk1_0,empty_set,esk2_0)
| ~ relstr_set_smaller(esk1_0,empty_set,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
relstr_element_smaller(esk1_0,empty_set,esk2_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( in(esk7_3(esk1_0,X1,esk2_0),X1)
| relstr_set_smaller(esk1_0,X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_11]),c_0_12])]) ).
cnf(c_0_20,negated_conjecture,
~ relstr_set_smaller(esk1_0,empty_set,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU355+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n005.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 06:14:47 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 46.21/7.25 % Version: 3.5.1
% 46.21/7.25 % Preprocessing class: FSLMSMSSSSSNFFN.
% 46.21/7.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 46.21/7.25 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 46.21/7.25 % Starting new_bool_3 with 600s (2) cores
% 46.21/7.25 % Starting new_bool_1 with 600s (2) cores
% 46.21/7.25 % Starting sh5l with 300s (1) cores
% 46.21/7.25 % new_bool_1 with pid 2730236 completed with status 0
% 46.21/7.25 % Result found by new_bool_1
% 46.21/7.25 % Preprocessing class: FSLMSMSSSSSNFFN.
% 46.21/7.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 46.21/7.25 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 46.21/7.25 % Starting new_bool_3 with 600s (2) cores
% 46.21/7.25 % Starting new_bool_1 with 600s (2) cores
% 46.21/7.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 46.21/7.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 46.21/7.25 % Search class: FGHSM-FMLM32-MFFFFFNN
% 46.21/7.25 % partial match(1): FGHSM-SMLM32-MFFFFFNN
% 46.21/7.25 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 46.21/7.25 % Starting SubtermCWHack with 55s (1) cores
% 46.21/7.25 % Starting new_bool_1 with 61s (1) cores
% 46.21/7.25 % new_bool_1 with pid 2730249 completed with status 0
% 46.21/7.25 % Result found by new_bool_1
% 46.21/7.25 % Preprocessing class: FSLMSMSSSSSNFFN.
% 46.21/7.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 46.21/7.25 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 46.21/7.25 % Starting new_bool_3 with 600s (2) cores
% 46.21/7.25 % Starting new_bool_1 with 600s (2) cores
% 46.21/7.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 46.21/7.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 46.21/7.25 % Search class: FGHSM-FMLM32-MFFFFFNN
% 46.21/7.25 % partial match(1): FGHSM-SMLM32-MFFFFFNN
% 46.21/7.25 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 46.21/7.25 % Starting SubtermCWHack with 55s (1) cores
% 46.21/7.25 % Starting new_bool_1 with 61s (1) cores
% 46.21/7.25 % Preprocessing time : 0.022 s
% 46.21/7.25 % Presaturation interreduction done
% 46.21/7.25
% 46.21/7.25 % Proof found!
% 46.21/7.25 % SZS status Theorem
% 46.21/7.25 % SZS output start CNFRefutation
% See solution above
% 46.21/7.25 % Parsed axioms : 671
% 46.21/7.25 % Removed by relevancy pruning/SinE : 537
% 46.21/7.25 % Initial clauses : 991
% 46.21/7.25 % Removed in clause preprocessing : 5
% 46.21/7.25 % Initial clauses in saturation : 986
% 46.21/7.25 % Processed clauses : 28034
% 46.21/7.25 % ...of these trivial : 31
% 46.21/7.25 % ...subsumed : 22931
% 46.21/7.25 % ...remaining for further processing : 5072
% 46.21/7.25 % Other redundant clauses eliminated : 1305
% 46.21/7.25 % Clauses deleted for lack of memory : 0
% 46.21/7.25 % Backward-subsumed : 252
% 46.21/7.25 % Backward-rewritten : 354
% 46.21/7.25 % Generated clauses : 197586
% 46.21/7.25 % ...of the previous two non-redundant : 185957
% 46.21/7.25 % ...aggressively subsumed : 0
% 46.21/7.25 % Contextual simplify-reflections : 348
% 46.21/7.25 % Paramodulations : 196404
% 46.21/7.25 % Factorizations : 4
% 46.21/7.25 % NegExts : 0
% 46.21/7.25 % Equation resolutions : 1307
% 46.21/7.25 % Disequality decompositions : 0
% 46.21/7.25 % Total rewrite steps : 26425
% 46.21/7.25 % ...of those cached : 25373
% 46.21/7.25 % Propositional unsat checks : 1
% 46.21/7.25 % Propositional check models : 0
% 46.21/7.25 % Propositional check unsatisfiable : 0
% 46.21/7.25 % Propositional clauses : 0
% 46.21/7.25 % Propositional clauses after purity: 0
% 46.21/7.25 % Propositional unsat core size : 0
% 46.21/7.25 % Propositional preprocessing time : 0.000
% 46.21/7.25 % Propositional encoding time : 0.338
% 46.21/7.25 % Propositional solver time : 0.172
% 46.21/7.25 % Success case prop preproc time : 0.000
% 46.21/7.25 % Success case prop encoding time : 0.000
% 46.21/7.25 % Success case prop solver time : 0.000
% 46.21/7.25 % Current number of processed clauses : 3208
% 46.21/7.25 % Positive orientable unit clauses : 93
% 46.21/7.25 % Positive unorientable unit clauses: 0
% 46.21/7.25 % Negative unit clauses : 57
% 46.21/7.25 % Non-unit-clauses : 3058
% 46.21/7.25 % Current number of unprocessed clauses: 158486
% 46.21/7.25 % ...number of literals in the above : 810375
% 46.21/7.25 % Current number of archived formulas : 0
% 46.21/7.25 % Current number of archived clauses : 1528
% 46.21/7.25 % Clause-clause subsumption calls (NU) : 2932222
% 46.21/7.25 % Rec. Clause-clause subsumption calls : 1222338
% 46.21/7.25 % Non-unit clause-clause subsumptions : 18362
% 46.21/7.25 % Unit Clause-clause subsumption calls : 12639
% 46.21/7.25 % Rewrite failures with RHS unbound : 0
% 46.21/7.25 % BW rewrite match attempts : 222
% 46.21/7.25 % BW rewrite match successes : 53
% 46.21/7.25 % Condensation attempts : 0
% 46.21/7.25 % Condensation successes : 0
% 46.21/7.25 % Termbank termtop insertions : 5669061
% 46.21/7.25 % Search garbage collected termcells : 16128
% 46.21/7.25
% 46.21/7.25 % -------------------------------------------------
% 46.21/7.25 % User time : 6.412 s
% 46.21/7.25 % System time : 0.190 s
% 46.21/7.25 % Total time : 6.602 s
% 46.21/7.25 % Maximum resident set size: 6608 pages
% 46.21/7.25
% 46.21/7.25 % -------------------------------------------------
% 46.21/7.25 % User time : 12.882 s
% 46.21/7.25 % System time : 0.409 s
% 46.21/7.25 % Total time : 13.291 s
% 46.21/7.25 % Maximum resident set size: 5888 pages
% 46.21/7.25 % E exiting
%------------------------------------------------------------------------------