%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU327+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 : n013.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 02:24:43 PM UTC 2026
% Result : Theorem 13.59s 2.29s
% Output : CNFRefutation 13.59s
% 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(t11_tops_2,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tops_2) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(t47_setfam_1,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(dt_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_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
=> meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[t11_tops_2]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_10,plain,
! [X843,X844] :
( union_of_subsets(X843,X844) = union(X844)
| ~ element(X844,powerset(powerset(X843))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])])]) ).
fof(c_0_11,negated_conjecture,
( meet_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,union_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
=> subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[t47_setfam_1]) ).
fof(c_0_13,plain,
! [X578,X579] :
( element(union_of_subsets(X578,X579),powerset(X578))
| ~ element(X579,powerset(powerset(X578))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])])]) ).
cnf(c_0_14,plain,
( ~ element(X1,powerset(powerset(X2)))
| union_of_subsets(X2,X1) = union(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,
! [X1538,X1539] :
( subset_difference(X1538,cast_to_subset(X1538),union_of_subsets(X1538,X1539)) = meet_of_subsets(X1538,complements_of_subsets(X1538,X1539))
| X1539 = empty_set
| ~ element(X1539,powerset(powerset(X1538))) ),
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(union_of_subsets(X2,X1),powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
union_of_subsets(esk312_0,esk313_0) = union(esk313_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,lemma,
( ~ element(X1,powerset(powerset(X2)))
| subset_difference(X2,cast_to_subset(X2),union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_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,
meet_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,union_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(union(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)))
| subset_difference(X2,X2,union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_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,
meet_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,union(esk313_0)),
inference(rw,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
subset_complement(esk312_0,union(esk313_0)) = set_difference(esk312_0,union(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,union(esk313_0)) = meet_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,
meet_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != set_difference(esk312_0,union(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 : SEU327+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n013.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 21 06:11:37 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 Running first-order theorem proving
% 0.18/0.43 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
% 13.59/2.29 % Version: 3.5.1
% 13.59/2.29 % Preprocessing class: FSLMSMSSSSSNFFN.
% 13.59/2.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.59/2.29 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 13.59/2.29 % Starting new_bool_3 with 600s (2) cores
% 13.59/2.29 % Starting new_bool_1 with 600s (2) cores
% 13.59/2.29 % Starting sh5l with 300s (1) cores
% 13.59/2.29 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 101210 completed with status 0
% 13.59/2.29 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 13.59/2.29 % Preprocessing class: FSLMSMSSSSSNFFN.
% 13.59/2.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.59/2.29 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 13.59/2.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.59/2.29 % No SInE strategy applied
% 13.59/2.29 % Search class: FGHSM-SMLM32-MFFFFFNN
% 13.59/2.29 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 13.59/2.29 % Starting SubtermCWHack with 82s (1) cores
% 13.59/2.29 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 13.59/2.29 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 13.59/2.29 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 101257 completed with status 0
% 13.59/2.29 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 13.59/2.29 % Preprocessing class: FSLMSMSSSSSNFFN.
% 13.59/2.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.59/2.29 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 13.59/2.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.59/2.29 % No SInE strategy applied
% 13.59/2.29 % Search class: FGHSM-SMLM32-MFFFFFNN
% 13.59/2.29 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 13.59/2.29 % Starting SubtermCWHack with 82s (1) cores
% 13.59/2.29 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 13.59/2.29 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 13.59/2.29 % Preprocessing time : 0.037 s
% 13.59/2.29 % Presaturation interreduction done
% 13.59/2.29
% 13.59/2.29 % Proof found!
% 13.59/2.29 % SZS status Theorem
% 13.59/2.29 % SZS output start CNFRefutation
% See solution above
% 13.59/2.29 % Parsed axioms : 540
% 13.59/2.29 % Removed by relevancy pruning/SinE : 0
% 13.59/2.29 % Initial clauses : 2094
% 13.59/2.29 % Removed in clause preprocessing : 40
% 13.59/2.29 % Initial clauses in saturation : 2054
% 13.59/2.29 % Processed clauses : 7660
% 13.59/2.29 % ...of these trivial : 101
% 13.59/2.29 % ...subsumed : 3113
% 13.59/2.29 % ...remaining for further processing : 4446
% 13.59/2.29 % Other redundant clauses eliminated : 571
% 13.59/2.29 % Clauses deleted for lack of memory : 0
% 13.59/2.29 % Backward-subsumed : 47
% 13.59/2.29 % Backward-rewritten : 94
% 13.59/2.29 % Generated clauses : 19273
% 13.59/2.29 % ...of the previous two non-redundant : 17637
% 13.59/2.29 % ...aggressively subsumed : 0
% 13.59/2.29 % Contextual simplify-reflections : 227
% 13.59/2.29 % Paramodulations : 18835
% 13.59/2.29 % Factorizations : 3
% 13.59/2.29 % NegExts : 0
% 13.59/2.29 % Equation resolutions : 574
% 13.59/2.29 % Disequality decompositions : 0
% 13.59/2.29 % Total rewrite steps : 3328
% 13.59/2.29 % ...of those cached : 2954
% 13.59/2.29 % Propositional unsat checks : 0
% 13.59/2.29 % Propositional check models : 0
% 13.59/2.29 % Propositional check unsatisfiable : 0
% 13.59/2.29 % Propositional clauses : 0
% 13.59/2.29 % Propositional clauses after purity: 0
% 13.59/2.29 % Propositional unsat core size : 0
% 13.59/2.29 % Propositional preprocessing time : 0.000
% 13.59/2.29 % Propositional encoding time : 0.000
% 13.59/2.29 % Propositional solver time : 0.000
% 13.59/2.29 % Success case prop preproc time : 0.000
% 13.59/2.29 % Success case prop encoding time : 0.000
% 13.59/2.29 % Success case prop solver time : 0.000
% 13.59/2.29 % Current number of processed clauses : 2008
% 13.59/2.29 % Positive orientable unit clauses : 244
% 13.59/2.29 % Positive unorientable unit clauses: 3
% 13.59/2.29 % Negative unit clauses : 411
% 13.59/2.29 % Non-unit-clauses : 1350
% 13.59/2.29 % Current number of unprocessed clauses: 13629
% 13.59/2.29 % ...number of literals in the above : 44430
% 13.59/2.29 % Current number of archived formulas : 0
% 13.59/2.29 % Current number of archived clauses : 2049
% 13.59/2.29 % Clause-clause subsumption calls (NU) : 2557778
% 13.59/2.29 % Rec. Clause-clause subsumption calls : 541931
% 13.59/2.29 % Non-unit clause-clause subsumptions : 1510
% 13.59/2.29 % Unit Clause-clause subsumption calls : 38968
% 13.59/2.29 % Rewrite failures with RHS unbound : 0
% 13.59/2.29 % BW rewrite match attempts : 130
% 13.59/2.29 % BW rewrite match successes : 90
% 13.59/2.29 % Condensation attempts : 0
% 13.59/2.29 % Condensation successes : 0
% 13.59/2.29 % Termbank termtop insertions : 362402
% 13.59/2.29 % Search garbage collected termcells : 29065
% 13.59/2.29
% 13.59/2.29 % -------------------------------------------------
% 13.59/2.29 % User time : 1.645 s
% 13.59/2.29 % System time : 0.032 s
% 13.59/2.29 % Total time : 1.676 s
% 13.59/2.29 % Maximum resident set size: 9208 pages
% 13.59/2.29
% 13.59/2.29 % -------------------------------------------------
% 13.59/2.29 % User time : 4.959 s
% 13.59/2.29 % System time : 0.113 s
% 13.59/2.29 % Total time : 5.072 s
% 13.59/2.29 % Maximum resident set size: 5632 pages
% 13.59/2.29 % E exiting
%------------------------------------------------------------------------------