%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU321+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 : n015.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 02:24:42 PM UTC 2026
% Result : Theorem 0.17s 5.66s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 11 unt; 0 def)
% Number of atoms : 117 ( 5 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 134 ( 53 ~; 33 |; 17 &)
% ( 7 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l40_tops_1,conjecture,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l40_tops_1) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(t50_subset_1,lemma,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(t54_subset_1,lemma,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,X3)
& in(X2,subset_complement(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
inference(assume_negation,[status(cth)],[l40_tops_1]) ).
fof(c_0_8,plain,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_11,plain,
! [X173,X174] :
( ( ~ empty(X173)
| element(X174,X173)
| ~ empty(X174) )
& ( ~ empty(X173)
| empty(X174)
| ~ element(X174,X173) )
& ( empty(X173)
| element(X174,X173)
| ~ in(X174,X173) )
& ( empty(X173)
| in(X174,X173)
| ~ element(X174,X173) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_12,negated_conjecture,
( ( ~ in(esk3_0,esk2_0)
| in(esk3_0,subset_complement(the_carrier(esk1_0),esk2_0)) )
& ( in(esk3_0,esk2_0)
| ~ in(esk3_0,subset_complement(the_carrier(esk1_0),esk2_0)) )
& element(esk3_0,the_carrier(esk1_0))
& element(esk2_0,powerset(the_carrier(esk1_0)))
& one_sorted_str(esk1_0)
& ~ empty_carrier(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_13,plain,
! [X83] :
( ~ empty(the_carrier(X83))
| ~ one_sorted_str(X83)
| empty_carrier(X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_14,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
element(esk3_0,the_carrier(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,lemma,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t50_subset_1]) ).
fof(c_0_17,lemma,
! [X50,X51,X52] :
( ~ in(X51,X52)
| ~ in(X51,subset_complement(X50,X52))
| ~ element(X52,powerset(X50)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_subset_1])])]) ).
fof(c_0_18,plain,
! [X222,X223] :
( ~ empty(X223)
| ~ in(X222,X223) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
cnf(c_0_19,plain,
( ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( in(esk3_0,the_carrier(esk1_0))
| empty(the_carrier(esk1_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
one_sorted_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
~ empty_carrier(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_23,lemma,
! [X47,X48,X49] :
( in(X49,subset_complement(X47,X48))
| in(X49,X48)
| ~ element(X49,X47)
| ~ element(X48,powerset(X47))
| X47 = empty_set ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_24,lemma,
( ~ in(X3,X1)
| ~ in(X3,subset_complement(X2,X1))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(esk3_0,esk2_0)
| in(esk3_0,subset_complement(the_carrier(esk1_0),esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,negated_conjecture,
element(esk2_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,plain,
( ~ empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
in(esk3_0,the_carrier(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(esk3_0,subset_complement(the_carrier(esk1_0),esk2_0))
| in(esk3_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,lemma,
( ~ element(X3,X1)
| ~ element(X2,powerset(X1))
| in(X3,subset_complement(X1,X2))
| in(X3,X2)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
~ in(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_32,negated_conjecture,
~ empty(the_carrier(esk1_0)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
the_carrier(esk1_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_29,c_0_30]),c_0_26]),c_0_15])]),c_0_31]) ).
cnf(c_0_34,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU321+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 % Computer : n015.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Mon Sep 21 06:14:58 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.47 Running first-order theorem proving
% 0.13/5.47 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
% 0.17/5.66 % Version: 3.5.1
% 0.17/5.66 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.17/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.66 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.17/5.66 % Starting new_bool_3 with 600s (2) cores
% 0.17/5.66 % Starting new_bool_1 with 600s (2) cores
% 0.17/5.66 % Starting sh5l with 300s (1) cores
% 0.17/5.66 % new_bool_3 with pid 735693 completed with status 0
% 0.17/5.66 % Result found by new_bool_3
% 0.17/5.66 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.17/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.66 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.17/5.66 % Starting new_bool_3 with 600s (2) cores
% 0.17/5.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/5.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/5.66 % Search class: FGHSM-FSLM31-SFFFFFNN
% 0.17/5.66 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.17/5.66 % Starting SubtermCWHack with 55s (1) cores
% 0.17/5.66 % Starting new_bool_3 with 61s (1) cores
% 0.17/5.66 % SubtermCWHack with pid 735696 completed with status 0
% 0.17/5.66 % Result found by SubtermCWHack
% 0.17/5.66 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.17/5.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.66 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.17/5.66 % Starting new_bool_3 with 600s (2) cores
% 0.17/5.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/5.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/5.66 % Search class: FGHSM-FSLM31-SFFFFFNN
% 0.17/5.66 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.17/5.66 % Starting SubtermCWHack with 55s (1) cores
% 0.17/5.66 % Preprocessing time : 0.006 s
% 0.17/5.66
% 0.17/5.66 % Proof found!
% 0.17/5.66 % SZS status Theorem
% 0.17/5.66 % SZS output start CNFRefutation
% See solution above
% 0.17/5.66 % Parsed axioms : 523
% 0.17/5.66 % Removed by relevancy pruning/SinE : 390
% 0.17/5.66 % Initial clauses : 497
% 0.17/5.66 % Removed in clause preprocessing : 2
% 0.17/5.66 % Initial clauses in saturation : 495
% 0.17/5.66 % Processed clauses : 2148
% 0.17/5.66 % ...of these trivial : 5
% 0.17/5.66 % ...subsumed : 1431
% 0.17/5.66 % ...remaining for further processing : 712
% 0.17/5.66 % Other redundant clauses eliminated : 100
% 0.17/5.66 % Clauses deleted for lack of memory : 0
% 0.17/5.66 % Backward-subsumed : 6
% 0.17/5.66 % Backward-rewritten : 53
% 0.17/5.66 % Generated clauses : 5390
% 0.17/5.66 % ...of the previous two non-redundant : 4697
% 0.17/5.66 % ...aggressively subsumed : 0
% 0.17/5.66 % Contextual simplify-reflections : 0
% 0.17/5.66 % Paramodulations : 5285
% 0.17/5.66 % Factorizations : 2
% 0.17/5.66 % NegExts : 0
% 0.17/5.66 % Equation resolutions : 102
% 0.17/5.66 % Disequality decompositions : 0
% 0.17/5.66 % Total rewrite steps : 913
% 0.17/5.66 % ...of those cached : 823
% 0.17/5.66 % Propositional unsat checks : 0
% 0.17/5.66 % Propositional check models : 0
% 0.17/5.66 % Propositional check unsatisfiable : 0
% 0.17/5.66 % Propositional clauses : 0
% 0.17/5.66 % Propositional clauses after purity: 0
% 0.17/5.66 % Propositional unsat core size : 0
% 0.17/5.66 % Propositional preprocessing time : 0.000
% 0.17/5.66 % Propositional encoding time : 0.000
% 0.17/5.66 % Propositional solver time : 0.000
% 0.17/5.66 % Success case prop preproc time : 0.000
% 0.17/5.66 % Success case prop encoding time : 0.000
% 0.17/5.66 % Success case prop solver time : 0.000
% 0.17/5.66 % Current number of processed clauses : 604
% 0.17/5.66 % Positive orientable unit clauses : 64
% 0.17/5.66 % Positive unorientable unit clauses: 1
% 0.17/5.66 % Negative unit clauses : 58
% 0.17/5.66 % Non-unit-clauses : 481
% 0.17/5.66 % Current number of unprocessed clauses: 2993
% 0.17/5.66 % ...number of literals in the above : 10325
% 0.17/5.66 % Current number of archived formulas : 0
% 0.17/5.66 % Current number of archived clauses : 62
% 0.17/5.66 % Clause-clause subsumption calls (NU) : 91654
% 0.17/5.66 % Rec. Clause-clause subsumption calls : 75347
% 0.17/5.66 % Non-unit clause-clause subsumptions : 1185
% 0.17/5.66 % Unit Clause-clause subsumption calls : 2403
% 0.17/5.66 % Rewrite failures with RHS unbound : 0
% 0.17/5.66 % BW rewrite match attempts : 40
% 0.17/5.66 % BW rewrite match successes : 19
% 0.17/5.66 % Condensation attempts : 0
% 0.17/5.66 % Condensation successes : 0
% 0.17/5.66 % Termbank termtop insertions : 83956
% 0.17/5.66 % Search garbage collected termcells : 8903
% 0.17/5.66
% 0.17/5.66 % -------------------------------------------------
% 0.17/5.66 % User time : 0.117 s
% 0.17/5.66 % System time : 0.011 s
% 0.17/5.66 % Total time : 0.128 s
% 0.17/5.66 % Maximum resident set size: 5348 pages
% 0.17/5.66
% 0.17/5.66 % -------------------------------------------------
% 0.17/5.66 % User time : 0.239 s
% 0.17/5.66 % System time : 0.027 s
% 0.17/5.66 % Total time : 0.266 s
% 0.17/5.66 % Maximum resident set size: 5376 pages
% 0.17/5.66 % E exiting
%------------------------------------------------------------------------------