%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU325+2 : 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 : n002.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 02:28:59 PM UTC 2026
% Result : Theorem 3.25s 1.18s
% Output : CNFRefutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 21 unt; 0 def)
% Number of atoms : 111 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 100 ( 41 ~; 26 |; 16 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 7 sgn 33 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( empty(X2)
& element(X2,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_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/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(t5_tops_2,conjecture,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( X2 = empty_set
& is_a_cover_of_carrier(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tops_2) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(fc2_pre_topc,axiom,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(d8_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( is_a_cover_of_carrier(X1,X2)
<=> cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_pre_topc) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_11,plain,
! [X34] :
( X34 = empty_set
| ~ empty(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
fof(c_0_12,plain,
! [X62] :
( empty(esk10_1(X62))
& element(esk10_1(X62),powerset(X62)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_13,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
empty(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X227,X228] :
( element(union_of_subsets(X227,X228),powerset(X227))
| ~ element(X228,powerset(powerset(X227))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])])]) ).
cnf(c_0_16,plain,
element(esk10_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
esk10_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,plain,
! [X229,X230] :
( union_of_subsets(X229,X230) = union(X230)
| ~ element(X230,powerset(powerset(X229))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_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_15]) ).
cnf(c_0_20,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( ~ element(X1,powerset(powerset(X2)))
| union_of_subsets(X2,X1) = union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( X2 = empty_set
& is_a_cover_of_carrier(X1,X2) ) ) ),
inference(assume_negation,[status(cth)],[t5_tops_2]) ).
fof(c_0_23,plain,
! [X47,X48] :
( ( element(X47,powerset(X48))
| ~ subset(X47,X48) )
& ( subset(X47,X48)
| ~ element(X47,powerset(X48)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_24,plain,
element(union_of_subsets(X1,empty_set),powerset(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
union_of_subsets(X1,empty_set) = union(empty_set),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
fof(c_0_26,negated_conjecture,
~ ! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( X2 = empty_set
& is_a_cover_of_carrier(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_27,lemma,
! [X28] :
( X28 = empty_set
| ~ subset(X28,empty_set) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])])]) ).
cnf(c_0_28,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
element(union(empty_set),powerset(X1)),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_30,plain,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_pre_topc]) ).
fof(c_0_31,plain,
! [X235] :
( cast_as_carrier_subset(X235) = the_carrier(X235)
| ~ one_sorted_str(X235) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])])]) ).
fof(c_0_32,negated_conjecture,
( esk2_0 = empty_set
& is_a_cover_of_carrier(esk1_0,esk2_0)
& element(esk2_0,powerset(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_26])])])]) ).
cnf(c_0_33,lemma,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
subset(union(empty_set),X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_35,plain,
! [X237] :
( ~ empty(cast_as_carrier_subset(X237))
| ~ one_sorted_str(X237)
| empty_carrier(X237) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_36,plain,
( ~ one_sorted_str(X1)
| cast_as_carrier_subset(X1) = the_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
one_sorted_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_38,plain,
! [X35,X36] :
( ( ~ one_sorted_str(X35)
| ~ element(X36,powerset(powerset(the_carrier(X35))))
| is_a_cover_of_carrier(X35,X36)
| cast_as_carrier_subset(X35) != union_of_subsets(the_carrier(X35),X36) )
& ( ~ one_sorted_str(X35)
| ~ element(X36,powerset(powerset(the_carrier(X35))))
| cast_as_carrier_subset(X35) = union_of_subsets(the_carrier(X35),X36)
| ~ is_a_cover_of_carrier(X35,X36) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_pre_topc])])])])]) ).
cnf(c_0_39,negated_conjecture,
is_a_cover_of_carrier(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
esk2_0 = empty_set,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,lemma,
union(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
( ~ empty(cast_as_carrier_subset(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,negated_conjecture,
cast_as_carrier_subset(esk1_0) = the_carrier(esk1_0),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
~ empty_carrier(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ is_a_cover_of_carrier(X1,X2)
| cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,negated_conjecture,
is_a_cover_of_carrier(esk1_0,empty_set),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
union_of_subsets(X1,empty_set) = empty_set,
inference(rw,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
~ empty(the_carrier(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_37])]),c_0_44]) ).
cnf(c_0_49,negated_conjecture,
the_carrier(esk1_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_43]),c_0_37]),c_0_20])]) ).
cnf(c_0_50,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU325+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n002.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 06:14:31 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.53 Running first-order theorem proving
% 0.26/0.53 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
% 3.25/1.18 % Version: 3.5.1
% 3.25/1.18 % Preprocessing class: FSLMSMSSSSSNFFN.
% 3.25/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.25/1.18 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 3.25/1.18 % Starting new_bool_3 with 600s (2) cores
% 3.25/1.18 % Starting new_bool_1 with 600s (2) cores
% 3.25/1.18 % Starting sh5l with 300s (1) cores
% 3.25/1.18 % new_bool_3 with pid 2602678 completed with status 0
% 3.25/1.18 % Result found by new_bool_3
% 3.25/1.18 % Preprocessing class: FSLMSMSSSSSNFFN.
% 3.25/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.25/1.18 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 3.25/1.18 % Starting new_bool_3 with 600s (2) cores
% 3.25/1.18 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.25/1.18 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.25/1.18 % Search class: FGHSM-FSLM32-MFFFFFNN
% 3.25/1.18 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 3.25/1.18 % Starting SubtermCWHack with 55s (1) cores
% 3.25/1.18 % Starting new_bool_3 with 61s (1) cores
% 3.25/1.18 % new_bool_3 with pid 2602682 completed with status 0
% 3.25/1.18 % Result found by new_bool_3
% 3.25/1.18 % Preprocessing class: FSLMSMSSSSSNFFN.
% 3.25/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.25/1.18 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 3.25/1.18 % Starting new_bool_3 with 600s (2) cores
% 3.25/1.18 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.25/1.18 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.25/1.18 % Search class: FGHSM-FSLM32-MFFFFFNN
% 3.25/1.18 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 3.25/1.18 % Starting SubtermCWHack with 55s (1) cores
% 3.25/1.18 % Starting new_bool_3 with 61s (1) cores
% 3.25/1.18 % Preprocessing time : 0.024 s
% 3.25/1.18 % Presaturation interreduction done
% 3.25/1.18
% 3.25/1.18 % Proof found!
% 3.25/1.18 % SZS status Theorem
% 3.25/1.18 % SZS output start CNFRefutation
% See solution above
% 3.25/1.18 % Parsed axioms : 538
% 3.25/1.18 % Removed by relevancy pruning/SinE : 390
% 3.25/1.18 % Initial clauses : 724
% 3.25/1.18 % Removed in clause preprocessing : 2
% 3.25/1.18 % Initial clauses in saturation : 722
% 3.25/1.18 % Processed clauses : 1624
% 3.25/1.18 % ...of these trivial : 8
% 3.25/1.18 % ...subsumed : 418
% 3.25/1.18 % ...remaining for further processing : 1198
% 3.25/1.18 % Other redundant clauses eliminated : 289
% 3.25/1.18 % Clauses deleted for lack of memory : 0
% 3.25/1.18 % Backward-subsumed : 12
% 3.25/1.18 % Backward-rewritten : 29
% 3.25/1.18 % Generated clauses : 1989
% 3.25/1.18 % ...of the previous two non-redundant : 1659
% 3.25/1.18 % ...aggressively subsumed : 0
% 3.25/1.18 % Contextual simplify-reflections : 127
% 3.25/1.18 % Paramodulations : 1717
% 3.25/1.18 % Factorizations : 0
% 3.25/1.18 % NegExts : 0
% 3.25/1.18 % Equation resolutions : 291
% 3.25/1.18 % Disequality decompositions : 0
% 3.25/1.18 % Total rewrite steps : 446
% 3.25/1.18 % ...of those cached : 351
% 3.25/1.18 % Propositional unsat checks : 0
% 3.25/1.18 % Propositional check models : 0
% 3.25/1.18 % Propositional check unsatisfiable : 0
% 3.25/1.18 % Propositional clauses : 0
% 3.25/1.18 % Propositional clauses after purity: 0
% 3.25/1.18 % Propositional unsat core size : 0
% 3.25/1.18 % Propositional preprocessing time : 0.000
% 3.25/1.18 % Propositional encoding time : 0.000
% 3.25/1.18 % Propositional solver time : 0.000
% 3.25/1.18 % Success case prop preproc time : 0.000
% 3.25/1.18 % Success case prop encoding time : 0.000
% 3.25/1.18 % Success case prop solver time : 0.000
% 3.25/1.18 % Current number of processed clauses : 282
% 3.25/1.18 % Positive orientable unit clauses : 62
% 3.25/1.18 % Positive unorientable unit clauses: 1
% 3.25/1.18 % Negative unit clauses : 23
% 3.25/1.18 % Non-unit-clauses : 196
% 3.25/1.18 % Current number of unprocessed clauses: 1396
% 3.25/1.18 % ...number of literals in the above : 5426
% 3.25/1.18 % Current number of archived formulas : 0
% 3.25/1.18 % Current number of archived clauses : 713
% 3.25/1.18 % Clause-clause subsumption calls (NU) : 273484
% 3.25/1.18 % Rec. Clause-clause subsumption calls : 24027
% 3.25/1.18 % Non-unit clause-clause subsumptions : 383
% 3.25/1.18 % Unit Clause-clause subsumption calls : 506
% 3.25/1.18 % Rewrite failures with RHS unbound : 0
% 3.25/1.18 % BW rewrite match attempts : 37
% 3.25/1.18 % BW rewrite match successes : 19
% 3.25/1.18 % Condensation attempts : 0
% 3.25/1.18 % Condensation successes : 0
% 3.25/1.18 % Termbank termtop insertions : 81674
% 3.25/1.18 % Search garbage collected termcells : 12123
% 3.25/1.18
% 3.25/1.18 % -------------------------------------------------
% 3.25/1.18 % User time : 0.446 s
% 3.25/1.18 % System time : 0.015 s
% 3.25/1.18 % Total time : 0.461 s
% 3.25/1.18 % Maximum resident set size: 5312 pages
% 3.25/1.18
% 3.25/1.18 % -------------------------------------------------
% 3.25/1.18 % User time : 0.968 s
% 3.25/1.18 % System time : 0.052 s
% 3.25/1.18 % Total time : 1.019 s
% 3.25/1.18 % Maximum resident set size: 5376 pages
% 3.25/1.18 % E exiting
%------------------------------------------------------------------------------