%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU309+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 : n001.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 02:24:39 PM UTC 2026
% Result : Theorem 0.18s 1.17s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 50 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 18 ~; 12 |; 3 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 36 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t22_pre_topc,conjecture,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pre_topc) ).
fof(t17_pre_topc,lemma,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_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(c_0_6,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
inference(assume_negation,[status(cth)],[t22_pre_topc]) ).
fof(c_0_7,negated_conjecture,
( subset_difference(the_carrier(esk287_0),cast_as_carrier_subset(esk287_0),subset_difference(the_carrier(esk287_0),cast_as_carrier_subset(esk287_0),esk288_0)) != esk288_0
& element(esk288_0,powerset(the_carrier(esk287_0)))
& one_sorted_str(esk287_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_8,lemma,
! [X1221,X1222] :
( subset_complement(the_carrier(X1221),X1222) = subset_difference(the_carrier(X1221),cast_as_carrier_subset(X1221),X1222)
| ~ element(X1222,powerset(the_carrier(X1221)))
| ~ one_sorted_str(X1221) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_pre_topc])])])]) ).
cnf(c_0_9,negated_conjecture,
subset_difference(the_carrier(esk287_0),cast_as_carrier_subset(esk287_0),subset_difference(the_carrier(esk287_0),cast_as_carrier_subset(esk287_0),esk288_0)) != esk288_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,lemma,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ one_sorted_str(X1)
| subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
one_sorted_str(esk287_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
element(esk288_0,powerset(the_carrier(esk287_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
subset_difference(the_carrier(esk287_0),cast_as_carrier_subset(esk287_0),subset_complement(the_carrier(esk287_0),esk288_0)) != esk288_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]) ).
fof(c_0_14,plain,
! [X675,X676] :
( subset_complement(X675,subset_complement(X675,X676)) = X676
| ~ element(X676,powerset(X675)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])])]) ).
fof(c_0_15,plain,
! [X1376,X1377] :
( ( element(X1376,powerset(X1377))
| ~ subset(X1376,X1377) )
& ( subset(X1376,X1377)
| ~ element(X1376,powerset(X1377)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_16,lemma,
! [X1356,X1357] : subset(set_difference(X1356,X1357),X1356),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_17,lemma,
( ~ element(subset_complement(the_carrier(esk287_0),esk288_0),powerset(the_carrier(esk287_0)))
| subset_complement(the_carrier(esk287_0),subset_complement(the_carrier(esk287_0),esk288_0)) != esk288_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_10]),c_0_11])]) ).
cnf(c_0_18,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,subset_complement(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X437,X438] :
( subset_complement(X437,X438) = set_difference(X437,X438)
| ~ element(X438,powerset(X437)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])])]) ).
cnf(c_0_20,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,lemma,
~ element(subset_complement(the_carrier(esk287_0),esk288_0),powerset(the_carrier(esk287_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12])]) ).
cnf(c_0_23,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,lemma,
element(set_difference(X1,X2),powerset(X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU309+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 : n001.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 06:16:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.18/1.17 % Version: 3.5.1
% 0.18/1.17 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.18/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/1.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.18/1.17 % Starting new_bool_3 with 600s (2) cores
% 0.18/1.17 % Starting new_bool_1 with 600s (2) cores
% 0.18/1.17 % Starting sh5l with 300s (1) cores
% 0.18/1.17 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 2366995 completed with status 0
% 0.18/1.17 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 0.18/1.17 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.18/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/1.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.18/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/1.17 % No SInE strategy applied
% 0.18/1.17 % Search class: FGHSM-SMLM32-MFFFFFNN
% 0.18/1.17 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 0.18/1.17 % Starting SubtermCWHack with 82s (1) cores
% 0.18/1.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 0.18/1.17 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 0.18/1.17 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 2367005 completed with status 0
% 0.18/1.17 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 0.18/1.17 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.18/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/1.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.18/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/1.17 % No SInE strategy applied
% 0.18/1.17 % Search class: FGHSM-SMLM32-MFFFFFNN
% 0.18/1.17 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 0.18/1.17 % Starting SubtermCWHack with 82s (1) cores
% 0.18/1.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 0.18/1.17 % Preprocessing time : 0.020 s
% 0.18/1.17 % Presaturation interreduction done
% 0.18/1.17
% 0.18/1.17 % Proof found!
% 0.18/1.17 % SZS status Theorem
% 0.18/1.17 % SZS output start CNFRefutation
% See solution above
% 0.18/1.17 % Parsed axioms : 496
% 0.18/1.17 % Removed by relevancy pruning/SinE : 0
% 0.18/1.17 % Initial clauses : 1885
% 0.18/1.17 % Removed in clause preprocessing : 40
% 0.18/1.17 % Initial clauses in saturation : 1845
% 0.18/1.17 % Processed clauses : 5538
% 0.18/1.17 % ...of these trivial : 67
% 0.18/1.17 % ...subsumed : 1881
% 0.18/1.17 % ...remaining for further processing : 3590
% 0.18/1.17 % Other redundant clauses eliminated : 530
% 0.18/1.17 % Clauses deleted for lack of memory : 0
% 0.18/1.17 % Backward-subsumed : 109
% 0.18/1.17 % Backward-rewritten : 58
% 0.18/1.17 % Generated clauses : 8523
% 0.18/1.17 % ...of the previous two non-redundant : 7331
% 0.18/1.17 % ...aggressively subsumed : 0
% 0.18/1.17 % Contextual simplify-reflections : 201
% 0.18/1.17 % Paramodulations : 8119
% 0.18/1.17 % Factorizations : 0
% 0.18/1.17 % NegExts : 0
% 0.18/1.17 % Equation resolutions : 533
% 0.18/1.17 % Disequality decompositions : 0
% 0.18/1.17 % Total rewrite steps : 2181
% 0.18/1.17 % ...of those cached : 1906
% 0.18/1.17 % Propositional unsat checks : 0
% 0.18/1.17 % Propositional check models : 0
% 0.18/1.17 % Propositional check unsatisfiable : 0
% 0.18/1.17 % Propositional clauses : 0
% 0.18/1.17 % Propositional clauses after purity: 0
% 0.18/1.17 % Propositional unsat core size : 0
% 0.18/1.17 % Propositional preprocessing time : 0.000
% 0.18/1.17 % Propositional encoding time : 0.000
% 0.18/1.17 % Propositional solver time : 0.000
% 0.18/1.17 % Success case prop preproc time : 0.000
% 0.18/1.17 % Success case prop encoding time : 0.000
% 0.18/1.17 % Success case prop solver time : 0.000
% 0.18/1.17 % Current number of processed clauses : 1355
% 0.18/1.17 % Positive orientable unit clauses : 173
% 0.18/1.17 % Positive unorientable unit clauses: 3
% 0.18/1.17 % Negative unit clauses : 217
% 0.18/1.17 % Non-unit-clauses : 962
% 0.18/1.17 % Current number of unprocessed clauses: 5084
% 0.18/1.17 % ...number of literals in the above : 16098
% 0.18/1.17 % Current number of archived formulas : 0
% 0.18/1.17 % Current number of archived clauses : 1871
% 0.18/1.17 % Clause-clause subsumption calls (NU) : 2053890
% 0.18/1.17 % Rec. Clause-clause subsumption calls : 437650
% 0.18/1.17 % Non-unit clause-clause subsumptions : 1218
% 0.18/1.17 % Unit Clause-clause subsumption calls : 17049
% 0.18/1.17 % Rewrite failures with RHS unbound : 0
% 0.18/1.17 % BW rewrite match attempts : 107
% 0.18/1.17 % BW rewrite match successes : 72
% 0.18/1.17 % Condensation attempts : 0
% 0.18/1.17 % Condensation successes : 0
% 0.18/1.17 % Termbank termtop insertions : 234166
% 0.18/1.17 % Search garbage collected termcells : 25773
% 0.18/1.17
% 0.18/1.17 % -------------------------------------------------
% 0.18/1.17 % User time : 0.695 s
% 0.18/1.17 % System time : 0.018 s
% 0.18/1.17 % Total time : 0.713 s
% 0.18/1.17 % Maximum resident set size: 8632 pages
% 0.18/1.17
% 0.18/1.17 % -------------------------------------------------
% 0.18/1.17 % User time : 1.739 s
% 0.18/1.17 % System time : 0.059 s
% 0.18/1.17 % Total time : 1.799 s
% 0.18/1.17 % Maximum resident set size: 5120 pages
% 0.18/1.17 % E exiting
%------------------------------------------------------------------------------