%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU354+1 : 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 : n017.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 02:24:49 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 49 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 47 ( 21 ~; 10 |; 6 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_tex_2,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
fof(d2_tex_2,axiom,
! [X1,X2] :
( element(X2,X1)
=> ( proper_element(X2,X1)
<=> X2 != union(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
fof(rc2_tex_2,axiom,
! [X1] :
? [X2] :
( ~ proper_element(X2,powerset(X1))
& element(X2,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_2) ).
fof(t99_zfmisc_1,axiom,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
inference(assume_negation,[status(cth)],[t5_tex_2]) ).
fof(c_0_5,plain,
! [X1,X2] :
( element(X2,X1)
=> ( proper_element(X2,X1)
<=> X2 != union(X1) ) ),
inference(fof_simplification,[status(thm)],[d2_tex_2]) ).
fof(c_0_6,plain,
! [X1] :
? [X2] :
( ~ proper_element(X2,powerset(X1))
& element(X2,powerset(X1)) ),
inference(fof_simplification,[status(thm)],[rc2_tex_2]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_8,plain,
! [X6,X7] :
( ( ~ element(X7,X6)
| proper_element(X7,X6)
| X7 = union(X6) )
& ( ~ element(X7,X6)
| X7 != union(X6)
| ~ proper_element(X7,X6) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_9,plain,
! [X8] :
( ~ proper_element(esk3_1(X8),powerset(X8))
& element(esk3_1(X8),powerset(X8)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X14] : union(powerset(X14)) = X14,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
fof(c_0_11,negated_conjecture,
( ( esk2_0 != esk1_0
| proper_element(esk2_0,powerset(esk1_0)) )
& ( esk2_0 = esk1_0
| ~ proper_element(esk2_0,powerset(esk1_0)) )
& element(esk2_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_7])])])]) ).
cnf(c_0_12,plain,
( ~ element(X1,X2)
| proper_element(X1,X2)
| X1 = union(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
element(esk3_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
~ proper_element(esk3_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( ~ proper_element(esk2_0,powerset(esk1_0))
| esk2_0 = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
esk3_1(X1) = X1,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( esk2_0 != esk1_0
| proper_element(esk2_0,powerset(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
esk1_0 = esk2_0,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_14]),c_0_17]) ).
cnf(c_0_21,plain,
~ proper_element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 06:10:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % new_bool_1 with pid 1602814 completed with status 0
% 0.14/0.43 % Result found by new_bool_1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGHSS-FFSF21-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % SubtermCWHack with pid 1602818 completed with status 0
% 0.14/0.43 % Result found by SubtermCWHack
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGHSS-FFSF21-SFFFFFNN
% 0.14/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 43
% 0.14/0.43 % Removed by relevancy pruning/SinE : 36
% 0.14/0.43 % Initial clauses : 11
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 11
% 0.14/0.43 % Processed clauses : 13
% 0.14/0.43 % ...of these trivial : 0
% 0.14/0.43 % ...subsumed : 0
% 0.14/0.43 % ...remaining for further processing : 13
% 0.14/0.43 % Other redundant clauses eliminated : 1
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 0
% 0.14/0.43 % Backward-rewritten : 4
% 0.14/0.43 % Generated clauses : 7
% 0.14/0.43 % ...of the previous two non-redundant : 6
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 1
% 0.14/0.43 % Paramodulations : 6
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 1
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 9
% 0.14/0.43 % ...of those cached : 5
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 8
% 0.14/0.43 % Positive orientable unit clauses : 6
% 0.14/0.43 % Positive unorientable unit clauses: 0
% 0.14/0.43 % Negative unit clauses : 1
% 0.14/0.43 % Non-unit-clauses : 1
% 0.14/0.43 % Current number of unprocessed clauses: 4
% 0.14/0.43 % ...number of literals in the above : 8
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 4
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 1
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 1
% 0.14/0.43 % Non-unit clause-clause subsumptions : 1
% 0.14/0.43 % Unit Clause-clause subsumption calls : 1
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 3
% 0.14/0.43 % BW rewrite match successes : 2
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 1053
% 0.14/0.43 % Search garbage collected termcells : 334
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.003 s
% 0.14/0.43 % System time : 0.002 s
% 0.14/0.43 % Total time : 0.005 s
% 0.14/0.43 % Maximum resident set size: 3620 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.007 s
% 0.14/0.43 % System time : 0.005 s
% 0.14/0.43 % Total time : 0.012 s
% 0.14/0.43 % Maximum resident set size: 4864 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------