%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU328+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 : n007.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 9.51s 2.13s
% Output : CNFRefutation 9.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 17 unt; 0 def)
% Number of atoms : 71 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 26 ~; 16 |; 3 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',t12_tops_2) ).
fof(redefinition_k6_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> meet_of_subsets(X1,X2) = set_meet(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(t48_setfam_1,lemma,
! [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/sandbox2/benchmark/theBenchmark.p',t48_setfam_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/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(d4_subset_1,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(dt_k2_subset_1,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_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,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_10,plain,
! [X848,X849] :
( meet_of_subsets(X848,X849) = set_meet(X849)
| ~ element(X849,powerset(powerset(X848))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1])])]) ).
fof(c_0_11,negated_conjecture,
( union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,meet_of_subsets(esk312_0,esk313_0))
& esk313_0 != empty_set
& element(esk313_0,powerset(powerset(esk312_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_12,lemma,
! [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_13,plain,
! [X586,X587] :
( element(meet_of_subsets(X586,X587),powerset(X586))
| ~ element(X587,powerset(powerset(X586))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_setfam_1])])]) ).
cnf(c_0_14,plain,
( ~ element(X1,powerset(powerset(X2)))
| meet_of_subsets(X2,X1) = set_meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
element(esk313_0,powerset(powerset(esk312_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,lemma,
! [X1544,X1545] :
( union_of_subsets(X1544,complements_of_subsets(X1544,X1545)) = subset_difference(X1544,cast_to_subset(X1544),meet_of_subsets(X1544,X1545))
| X1545 = empty_set
| ~ element(X1545,powerset(powerset(X1544))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_17,plain,
! [X405] : cast_to_subset(X405) = X405,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(c_0_18,plain,
! [X459,X460] :
( subset_complement(X459,X460) = set_difference(X459,X460)
| ~ element(X460,powerset(X459)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])])]) ).
cnf(c_0_19,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(meet_of_subsets(X2,X1),powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
meet_of_subsets(esk312_0,esk313_0) = set_meet(esk313_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,lemma,
( ~ 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_16]) ).
cnf(c_0_22,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X558] : element(cast_to_subset(X558),powerset(X558)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
cnf(c_0_24,negated_conjecture,
union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,meet_of_subsets(esk312_0,esk313_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
element(set_meet(esk313_0),powerset(esk312_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_15])]) ).
fof(c_0_27,plain,
! [X850,X851,X852] :
( subset_difference(X850,X851,X852) = set_difference(X851,X852)
| ~ element(X852,powerset(X850))
| ~ element(X851,powerset(X850)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])])]) ).
cnf(c_0_28,lemma,
( ~ element(X1,powerset(powerset(X2)))
| union_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_difference(X2,X2,meet_of_subsets(X2,X1))
| X1 = empty_set ),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
esk313_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,set_meet(esk313_0)),
inference(rw,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
subset_complement(esk312_0,set_meet(esk313_0)) = set_difference(esk312_0,set_meet(esk313_0)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,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_27]) ).
cnf(c_0_34,negated_conjecture,
subset_difference(esk312_0,esk312_0,set_meet(esk313_0)) = union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_15])]),c_0_29]) ).
cnf(c_0_35,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_36,negated_conjecture,
union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != set_difference(esk312_0,set_meet(esk313_0)),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_26]),c_0_35])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU328+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 06:10:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 9.51/2.13 % Version: 3.5.1
% 9.51/2.13 % Preprocessing class: FSLMSMSSSSSNFFN.
% 9.51/2.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.51/2.13 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 9.51/2.13 % Starting new_bool_3 with 600s (2) cores
% 9.51/2.13 % Starting new_bool_1 with 600s (2) cores
% 9.51/2.13 % Starting sh5l with 300s (1) cores
% 9.51/2.13 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 350258 completed with status 0
% 9.51/2.13 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 9.51/2.13 % Preprocessing class: FSLMSMSSSSSNFFN.
% 9.51/2.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.51/2.13 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 9.51/2.13 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.51/2.13 % No SInE strategy applied
% 9.51/2.13 % Search class: FGHSM-SMLM32-MFFFFFNN
% 9.51/2.13 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 9.51/2.13 % Starting SubtermCWHack with 82s (1) cores
% 9.51/2.13 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 9.51/2.13 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 9.51/2.13 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 350269 completed with status 0
% 9.51/2.13 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 9.51/2.13 % Preprocessing class: FSLMSMSSSSSNFFN.
% 9.51/2.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.51/2.13 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 9.51/2.13 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.51/2.13 % No SInE strategy applied
% 9.51/2.13 % Search class: FGHSM-SMLM32-MFFFFFNN
% 9.51/2.13 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 9.51/2.13 % Starting SubtermCWHack with 82s (1) cores
% 9.51/2.13 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 9.51/2.13 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 9.51/2.13 % Preprocessing time : 0.038 s
% 9.51/2.13 % Presaturation interreduction done
% 9.51/2.13
% 9.51/2.13 % Proof found!
% 9.51/2.13 % SZS status Theorem
% 9.51/2.13 % SZS output start CNFRefutation
% See solution above
% 9.51/2.13 % Parsed axioms : 541
% 9.51/2.13 % Removed by relevancy pruning/SinE : 0
% 9.51/2.13 % Initial clauses : 2095
% 9.51/2.13 % Removed in clause preprocessing : 40
% 9.51/2.13 % Initial clauses in saturation : 2055
% 9.51/2.13 % Processed clauses : 7581
% 9.51/2.13 % ...of these trivial : 125
% 9.51/2.13 % ...subsumed : 3038
% 9.51/2.13 % ...remaining for further processing : 4418
% 9.51/2.13 % Other redundant clauses eliminated : 575
% 9.51/2.13 % Clauses deleted for lack of memory : 0
% 9.51/2.13 % Backward-subsumed : 62
% 9.51/2.13 % Backward-rewritten : 85
% 9.51/2.13 % Generated clauses : 19164
% 9.51/2.13 % ...of the previous two non-redundant : 17550
% 9.51/2.13 % ...aggressively subsumed : 0
% 9.51/2.13 % Contextual simplify-reflections : 226
% 9.51/2.13 % Paramodulations : 18723
% 9.51/2.13 % Factorizations : 2
% 9.51/2.13 % NegExts : 0
% 9.51/2.13 % Equation resolutions : 578
% 9.51/2.13 % Disequality decompositions : 0
% 9.51/2.13 % Total rewrite steps : 3397
% 9.51/2.13 % ...of those cached : 3031
% 9.51/2.13 % Propositional unsat checks : 0
% 9.51/2.13 % Propositional check models : 0
% 9.51/2.13 % Propositional check unsatisfiable : 0
% 9.51/2.13 % Propositional clauses : 0
% 9.51/2.13 % Propositional clauses after purity: 0
% 9.51/2.13 % Propositional unsat core size : 0
% 9.51/2.13 % Propositional preprocessing time : 0.000
% 9.51/2.13 % Propositional encoding time : 0.000
% 9.51/2.13 % Propositional solver time : 0.000
% 9.51/2.13 % Success case prop preproc time : 0.000
% 9.51/2.13 % Success case prop encoding time : 0.000
% 9.51/2.13 % Success case prop solver time : 0.000
% 9.51/2.13 % Current number of processed clauses : 1973
% 9.51/2.13 % Positive orientable unit clauses : 238
% 9.51/2.13 % Positive unorientable unit clauses: 3
% 9.51/2.13 % Negative unit clauses : 338
% 9.51/2.13 % Non-unit-clauses : 1394
% 9.51/2.13 % Current number of unprocessed clauses: 13640
% 9.51/2.13 % ...number of literals in the above : 45181
% 9.51/2.13 % Current number of archived formulas : 0
% 9.51/2.13 % Current number of archived clauses : 2056
% 9.51/2.13 % Clause-clause subsumption calls (NU) : 2579952
% 9.51/2.13 % Rec. Clause-clause subsumption calls : 558532
% 9.51/2.13 % Non-unit clause-clause subsumptions : 1600
% 9.51/2.13 % Unit Clause-clause subsumption calls : 33109
% 9.51/2.13 % Rewrite failures with RHS unbound : 0
% 9.51/2.13 % BW rewrite match attempts : 127
% 9.51/2.13 % BW rewrite match successes : 88
% 9.51/2.13 % Condensation attempts : 0
% 9.51/2.13 % Condensation successes : 0
% 9.51/2.13 % Termbank termtop insertions : 361804
% 9.51/2.13 % Search garbage collected termcells : 29080
% 9.51/2.13
% 9.51/2.13 % -------------------------------------------------
% 9.51/2.13 % User time : 1.521 s
% 9.51/2.13 % System time : 0.041 s
% 9.51/2.13 % Total time : 1.562 s
% 9.51/2.13 % Maximum resident set size: 9208 pages
% 9.51/2.13
% 9.51/2.13 % -------------------------------------------------
% 9.51/2.13 % User time : 3.654 s
% 9.51/2.13 % System time : 0.132 s
% 9.51/2.13 % Total time : 3.786 s
% 9.51/2.13 % Maximum resident set size: 5376 pages
% 9.51/2.13 % E exiting
%------------------------------------------------------------------------------