%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU328+1 : 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 : n017.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 02:24:44 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 64 ( 32 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 57 ( 25 ~; 16 |; 3 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t48_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(t12_tops_2,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_2) ).
fof(d4_subset_1,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(dt_k2_subset_1,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X3,powerset(X1))
& element(X2,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(dt_k6_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(c_0_7,plain,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[t48_setfam_1]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[t12_tops_2]) ).
fof(c_0_9,plain,
! [X14,X15] :
( union_of_subsets(X14,complements_of_subsets(X14,X15)) = subset_difference(X14,cast_to_subset(X14),meet_of_subsets(X14,X15))
| X15 = empty_set
| ~ element(X15,powerset(powerset(X14))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X43] : cast_to_subset(X43) = X43,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(c_0_11,plain,
! [X44] : element(cast_to_subset(X44),powerset(X44)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X40,X41,X42] :
( subset_difference(X40,X41,X42) = set_difference(X41,X42)
| ~ element(X42,powerset(X40))
| ~ element(X41,powerset(X40)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])])]) ).
cnf(c_0_14,plain,
( ~ element(X1,powerset(powerset(X2)))
| union_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_difference(X2,cast_to_subset(X2),meet_of_subsets(X2,X1))
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X12,X13] :
( element(meet_of_subsets(X12,X13),powerset(X12))
| ~ element(X13,powerset(powerset(X12))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_setfam_1])])]) ).
fof(c_0_18,negated_conjecture,
( union_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,meet_of_subsets(esk1_0,esk2_0))
& esk2_0 != empty_set
& element(esk2_0,powerset(powerset(esk1_0))) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_19,plain,
( ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2))
| subset_difference(X2,X1,X3) = set_difference(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ element(X2,powerset(powerset(X1)))
| X2 = empty_set
| subset_difference(X1,X1,meet_of_subsets(X1,X2)) = union_of_subsets(X1,complements_of_subsets(X1,X2)) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_22,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(meet_of_subsets(X2,X1),powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
union_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,meet_of_subsets(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ element(X2,powerset(powerset(X1)))
| X2 = empty_set
| union_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,meet_of_subsets(X1,X2)) ),
inference(csr,[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_25,negated_conjecture,
element(esk2_0,powerset(powerset(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X6,X7] :
( subset_complement(X6,X7) = set_difference(X6,X7)
| ~ element(X7,powerset(X6)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])])]) ).
cnf(c_0_28,negated_conjecture,
subset_complement(esk1_0,meet_of_subsets(esk1_0,esk2_0)) != set_difference(esk1_0,meet_of_subsets(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_29,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
~ element(meet_of_subsets(esk1_0,esk2_0),powerset(esk1_0)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_22]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU328+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.34 % Computer : n017.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 06:07:27 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % new_bool_3 with pid 1598286 completed with status 0
% 0.13/0.42 % Result found by new_bool_3
% 0.13/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.42 % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.13/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.42 % SubtermCWHack with pid 1598289 completed with status 0
% 0.13/0.42 % Result found by SubtermCWHack
% 0.13/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.42 % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.13/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.42 % Preprocessing time : 0.002 s
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 59
% 0.13/0.42 % Removed by relevancy pruning/SinE : 21
% 0.13/0.42 % Initial clauses : 76
% 0.13/0.42 % Removed in clause preprocessing : 0
% 0.13/0.42 % Initial clauses in saturation : 76
% 0.13/0.42 % Processed clauses : 423
% 0.13/0.42 % ...of these trivial : 1
% 0.13/0.42 % ...subsumed : 207
% 0.13/0.42 % ...remaining for further processing : 215
% 0.13/0.42 % Other redundant clauses eliminated : 0
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 0
% 0.13/0.42 % Backward-rewritten : 6
% 0.13/0.42 % Generated clauses : 638
% 0.13/0.42 % ...of the previous two non-redundant : 432
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 2
% 0.13/0.42 % Paramodulations : 638
% 0.13/0.42 % Factorizations : 0
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 0
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 339
% 0.13/0.42 % ...of those cached : 309
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 209
% 0.13/0.42 % Positive orientable unit clauses : 23
% 0.13/0.42 % Positive unorientable unit clauses: 0
% 0.13/0.42 % Negative unit clauses : 6
% 0.13/0.42 % Non-unit-clauses : 180
% 0.13/0.42 % Current number of unprocessed clauses: 85
% 0.13/0.42 % ...number of literals in the above : 351
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 6
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 4112
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 3847
% 0.13/0.42 % Non-unit clause-clause subsumptions : 209
% 0.13/0.42 % Unit Clause-clause subsumption calls : 13
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 9
% 0.13/0.42 % BW rewrite match successes : 1
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 11278
% 0.13/0.42 % Search garbage collected termcells : 661
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.020 s
% 0.13/0.42 % System time : 0.002 s
% 0.13/0.42 % Total time : 0.022 s
% 0.13/0.42 % Maximum resident set size: 3684 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.022 s
% 0.13/0.42 % System time : 0.007 s
% 0.13/0.42 % Total time : 0.029 s
% 0.13/0.42 % Maximum resident set size: 4864 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------