%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:23:50 PM UTC 2026
% Result : Theorem 0.16s 5.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 87 ( 8 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 95 ( 38 ~; 41 |; 9 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 52 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_finsub_1,axiom,
! [X1,X2] :
( preboolean(X2)
=> ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( finite(X3)
& subset(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [X1] : preboolean(finite_subsets(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t26_finsub_1,conjecture,
! [X1] : subset(finite_subsets(X1),powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(c_0_7,plain,
! [X11,X12,X13,X14] :
( ( ~ preboolean(X12)
| X12 = finite_subsets(X11)
| in(esk3_2(X11,X12),X12)
| finite(esk3_2(X11,X12)) )
& ( ~ preboolean(X12)
| X12 = finite_subsets(X11)
| in(esk3_2(X11,X12),X12)
| subset(esk3_2(X11,X12),X11) )
& ( ~ preboolean(X12)
| X12 = finite_subsets(X11)
| ~ finite(esk3_2(X11,X12))
| ~ subset(esk3_2(X11,X12),X11)
| ~ in(esk3_2(X11,X12),X12) )
& ( ~ preboolean(X12)
| X12 != finite_subsets(X11)
| in(X14,X12)
| ~ finite(X14)
| ~ subset(X14,X11) )
& ( ~ preboolean(X12)
| X12 != finite_subsets(X11)
| ~ in(X13,X12)
| finite(X13) )
& ( ~ preboolean(X12)
| X12 != finite_subsets(X11)
| ~ in(X13,X12)
| subset(X13,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_finsub_1])])])])])])]) ).
fof(c_0_8,plain,
! [X38] : preboolean(finite_subsets(X38)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
fof(c_0_9,plain,
! [X17,X18] :
( ( element(X17,powerset(X18))
| ~ subset(X17,X18) )
& ( subset(X17,X18)
| ~ element(X17,powerset(X18)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_10,plain,
( ~ preboolean(X3)
| X3 != finite_subsets(X2)
| ~ in(X1,X3)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_13,plain,
! [X44,X45] :
( in(X44,X45)
| empty(X45)
| ~ element(X44,X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_14,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ in(X1,finite_subsets(X2))
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11])]) ).
fof(c_0_16,plain,
! [X21] : ~ empty(powerset(X21)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])]) ).
cnf(c_0_17,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ in(X1,finite_subsets(X2))
| element(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X5,X6,X7,X8,X9] :
( ( subset(X8,X9)
| ~ in(esk2_2(X8,X9),X9) )
& ( subset(X8,X9)
| in(esk2_2(X8,X9),X8) )
& ( in(X7,X6)
| ~ in(X7,X5)
| ~ subset(X5,X6) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] : subset(finite_subsets(X1),powerset(X1)),
inference(assume_negation,[status(cth)],[t26_finsub_1]) ).
cnf(c_0_22,plain,
( ~ in(X1,finite_subsets(X2))
| in(X1,powerset(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,plain,
( subset(X1,X2)
| in(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,negated_conjecture,
~ subset(finite_subsets(esk1_0),powerset(esk1_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_25,plain,
( ~ in(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( in(esk2_2(finite_subsets(X1),X2),powerset(X1))
| subset(finite_subsets(X1),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
~ subset(finite_subsets(esk1_0),powerset(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
subset(finite_subsets(X1),powerset(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.38 % Computer : n007.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 05:48:41 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.45 % Version: 3.5.1
% 0.16/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.45 % Starting sh5l with 300s (1) cores
% 0.16/5.45 % new_bool_1 with pid 310364 completed with status 0
% 0.16/5.45 % Result found by new_bool_1
% 0.16/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/5.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/5.45 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.16/5.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/5.45 % Starting SubtermCWHack with 31s (1) cores
% 0.16/5.45 % SubtermCWHack with pid 310368 completed with status 0
% 0.16/5.45 % Result found by SubtermCWHack
% 0.16/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/5.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/5.45 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.16/5.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/5.45 % Starting SubtermCWHack with 31s (1) cores
% 0.16/5.45 % Preprocessing time : 0.001 s
% 0.16/5.45
% 0.16/5.45 % Proof found!
% 0.16/5.45 % SZS status Theorem
% 0.16/5.45 % SZS output start CNFRefutation
% See solution above
% 0.16/5.45 % Parsed axioms : 33
% 0.16/5.45 % Removed by relevancy pruning/SinE : 4
% 0.16/5.45 % Initial clauses : 51
% 0.16/5.45 % Removed in clause preprocessing : 0
% 0.16/5.45 % Initial clauses in saturation : 51
% 0.16/5.45 % Processed clauses : 188
% 0.16/5.45 % ...of these trivial : 1
% 0.16/5.45 % ...subsumed : 63
% 0.16/5.45 % ...remaining for further processing : 124
% 0.16/5.45 % Other redundant clauses eliminated : 3
% 0.16/5.45 % Clauses deleted for lack of memory : 0
% 0.16/5.45 % Backward-subsumed : 2
% 0.16/5.45 % Backward-rewritten : 5
% 0.16/5.45 % Generated clauses : 254
% 0.16/5.45 % ...of the previous two non-redundant : 201
% 0.16/5.45 % ...aggressively subsumed : 0
% 0.16/5.45 % Contextual simplify-reflections : 1
% 0.16/5.45 % Paramodulations : 251
% 0.16/5.45 % Factorizations : 0
% 0.16/5.45 % NegExts : 0
% 0.16/5.45 % Equation resolutions : 3
% 0.16/5.45 % Disequality decompositions : 0
% 0.16/5.45 % Total rewrite steps : 48
% 0.16/5.45 % ...of those cached : 28
% 0.16/5.45 % Propositional unsat checks : 0
% 0.16/5.45 % Propositional check models : 0
% 0.16/5.45 % Propositional check unsatisfiable : 0
% 0.16/5.45 % Propositional clauses : 0
% 0.16/5.45 % Propositional clauses after purity: 0
% 0.16/5.45 % Propositional unsat core size : 0
% 0.16/5.45 % Propositional preprocessing time : 0.000
% 0.16/5.45 % Propositional encoding time : 0.000
% 0.16/5.45 % Propositional solver time : 0.000
% 0.16/5.45 % Success case prop preproc time : 0.000
% 0.16/5.45 % Success case prop encoding time : 0.000
% 0.16/5.45 % Success case prop solver time : 0.000
% 0.16/5.45 % Current number of processed clauses : 114
% 0.16/5.45 % Positive orientable unit clauses : 21
% 0.16/5.45 % Positive unorientable unit clauses: 0
% 0.16/5.45 % Negative unit clauses : 11
% 0.16/5.45 % Non-unit-clauses : 82
% 0.16/5.45 % Current number of unprocessed clauses: 53
% 0.16/5.45 % ...number of literals in the above : 154
% 0.16/5.45 % Current number of archived formulas : 0
% 0.16/5.45 % Current number of archived clauses : 7
% 0.16/5.45 % Clause-clause subsumption calls (NU) : 646
% 0.16/5.45 % Rec. Clause-clause subsumption calls : 536
% 0.16/5.45 % Non-unit clause-clause subsumptions : 39
% 0.16/5.45 % Unit Clause-clause subsumption calls : 81
% 0.16/5.45 % Rewrite failures with RHS unbound : 0
% 0.16/5.45 % BW rewrite match attempts : 10
% 0.16/5.45 % BW rewrite match successes : 4
% 0.16/5.45 % Condensation attempts : 0
% 0.16/5.45 % Condensation successes : 0
% 0.16/5.45 % Termbank termtop insertions : 5459
% 0.16/5.45 % Search garbage collected termcells : 593
% 0.16/5.45
% 0.16/5.45 % -------------------------------------------------
% 0.16/5.45 % User time : 0.011 s
% 0.16/5.45 % System time : 0.002 s
% 0.16/5.45 % Total time : 0.012 s
% 0.16/5.45 % Maximum resident set size: 3660 pages
% 0.16/5.45
% 0.16/5.45 % -------------------------------------------------
% 0.16/5.45 % User time : 0.013 s
% 0.16/5.45 % System time : 0.006 s
% 0.16/5.45 % Total time : 0.018 s
% 0.16/5.45 % Maximum resident set size: 4608 pages
% 0.16/5.45 % E exiting
%------------------------------------------------------------------------------