%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU171+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 : n015.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 02:24:07 PM UTC 2026
% Result : Theorem 0.55s 0.52s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 105 ( 21 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 119 ( 43 ~; 34 |; 16 &)
% ( 8 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t50_subset_1,conjecture,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_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(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[t50_subset_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_8,plain,
! [X21,X22] :
( subset_complement(X21,X22) = set_difference(X21,X22)
| ~ element(X22,powerset(X21)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])])]) ).
fof(c_0_9,negated_conjecture,
( ~ in(esk3_0,subset_complement(esk1_0,esk2_0))
& ~ in(esk3_0,esk2_0)
& element(esk3_0,esk1_0)
& element(esk2_0,powerset(esk1_0))
& esk1_0 != empty_set ),
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_10,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_11,plain,
! [X30,X31] :
( ( ~ empty(X30)
| element(X31,X30)
| ~ empty(X31) )
& ( ~ empty(X30)
| empty(X31)
| ~ element(X31,X30) )
& ( empty(X30)
| element(X31,X30)
| ~ in(X31,X30) )
& ( empty(X30)
| in(X31,X30)
| ~ element(X31,X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_12,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X74,X75,X76,X77,X78,X79,X80,X81] :
( ( X81 = set_difference(X79,X80)
| in(esk11_3(X79,X80,X81),X81)
| ~ in(esk11_3(X79,X80,X81),X80) )
& ( X81 = set_difference(X79,X80)
| in(esk11_3(X79,X80,X81),X81)
| in(esk11_3(X79,X80,X81),X79) )
& ( X81 = set_difference(X79,X80)
| in(esk11_3(X79,X80,X81),X80)
| ~ in(esk11_3(X79,X80,X81),X79)
| ~ in(esk11_3(X79,X80,X81),X81) )
& ( X76 != set_difference(X74,X75)
| in(X78,X76)
| in(X78,X75)
| ~ in(X78,X74) )
& ( X76 != set_difference(X74,X75)
| ~ in(X77,X76)
| ~ in(X77,X75) )
& ( X76 != set_difference(X74,X75)
| ~ in(X77,X76)
| in(X77,X74) ) ),
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)],[c_0_10])])])])])])]) ).
fof(c_0_15,plain,
! [X67] :
( X67 = empty_set
| ~ empty(X67) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
cnf(c_0_16,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
element(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
~ in(esk3_0,subset_complement(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
subset_complement(esk1_0,esk2_0) = set_difference(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
( X4 != set_difference(X2,X3)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( in(esk3_0,esk1_0)
| empty(esk1_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
~ in(esk3_0,set_difference(esk1_0,esk2_0)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
in(esk3_0,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU171+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:57:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.55/0.52 % Version: 3.5.1
% 0.55/0.52 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.55/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.55/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.55/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.55/0.52 % Starting sh5l with 300s (1) cores
% 0.55/0.52 % new_bool_3 with pid 709893 completed with status 0
% 0.55/0.52 % Result found by new_bool_3
% 0.55/0.52 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.55/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.55/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.55/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.55/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.55/0.52 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.55/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.55/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.55/0.52 % SubtermCWHack with pid 709896 completed with status 0
% 0.55/0.52 % Result found by SubtermCWHack
% 0.55/0.52 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.55/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.52 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.55/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.55/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.55/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.55/0.52 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.55/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.55/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.55/0.52 % Preprocessing time : 0.001 s
% 0.55/0.52
% 0.55/0.52 % Proof found!
% 0.55/0.52 % SZS status Theorem
% 0.55/0.52 % SZS output start CNFRefutation
% See solution above
% 0.55/0.52 % Parsed axioms : 111
% 0.55/0.52 % Removed by relevancy pruning/SinE : 36
% 0.55/0.52 % Initial clauses : 126
% 0.55/0.52 % Removed in clause preprocessing : 0
% 0.55/0.52 % Initial clauses in saturation : 126
% 0.55/0.52 % Processed clauses : 2882
% 0.55/0.52 % ...of these trivial : 65
% 0.55/0.52 % ...subsumed : 2079
% 0.55/0.52 % ...remaining for further processing : 738
% 0.55/0.52 % Other redundant clauses eliminated : 87
% 0.55/0.52 % Clauses deleted for lack of memory : 0
% 0.55/0.52 % Backward-subsumed : 46
% 0.55/0.52 % Backward-rewritten : 17
% 0.55/0.52 % Generated clauses : 13599
% 0.55/0.52 % ...of the previous two non-redundant : 10556
% 0.55/0.52 % ...aggressively subsumed : 0
% 0.55/0.52 % Contextual simplify-reflections : 2
% 0.55/0.52 % Paramodulations : 13489
% 0.55/0.52 % Factorizations : 21
% 0.55/0.52 % NegExts : 0
% 0.55/0.52 % Equation resolutions : 87
% 0.55/0.52 % Disequality decompositions : 0
% 0.55/0.52 % Total rewrite steps : 4148
% 0.55/0.52 % ...of those cached : 3609
% 0.55/0.52 % Propositional unsat checks : 0
% 0.55/0.52 % Propositional check models : 0
% 0.55/0.52 % Propositional check unsatisfiable : 0
% 0.55/0.52 % Propositional clauses : 0
% 0.55/0.52 % Propositional clauses after purity: 0
% 0.55/0.52 % Propositional unsat core size : 0
% 0.55/0.52 % Propositional preprocessing time : 0.000
% 0.55/0.52 % Propositional encoding time : 0.000
% 0.55/0.52 % Propositional solver time : 0.000
% 0.55/0.52 % Success case prop preproc time : 0.000
% 0.55/0.52 % Success case prop encoding time : 0.000
% 0.55/0.52 % Success case prop solver time : 0.000
% 0.55/0.52 % Current number of processed clauses : 652
% 0.55/0.52 % Positive orientable unit clauses : 118
% 0.55/0.52 % Positive unorientable unit clauses: 2
% 0.55/0.52 % Negative unit clauses : 100
% 0.55/0.52 % Non-unit-clauses : 432
% 0.55/0.52 % Current number of unprocessed clauses: 7731
% 0.55/0.52 % ...number of literals in the above : 19912
% 0.55/0.52 % Current number of archived formulas : 0
% 0.55/0.52 % Current number of archived clauses : 66
% 0.55/0.52 % Clause-clause subsumption calls (NU) : 21193
% 0.55/0.52 % Rec. Clause-clause subsumption calls : 15205
% 0.55/0.52 % Non-unit clause-clause subsumptions : 1092
% 0.55/0.52 % Unit Clause-clause subsumption calls : 4904
% 0.55/0.52 % Rewrite failures with RHS unbound : 0
% 0.55/0.52 % BW rewrite match attempts : 108
% 0.55/0.52 % BW rewrite match successes : 28
% 0.55/0.52 % Condensation attempts : 0
% 0.55/0.52 % Condensation successes : 0
% 0.55/0.52 % Termbank termtop insertions : 112001
% 0.55/0.52 % Search garbage collected termcells : 1902
% 0.55/0.52
% 0.55/0.52 % -------------------------------------------------
% 0.55/0.52 % User time : 0.088 s
% 0.55/0.52 % System time : 0.011 s
% 0.55/0.52 % Total time : 0.099 s
% 0.55/0.52 % Maximum resident set size: 3988 pages
% 0.55/0.52
% 0.55/0.52 % -------------------------------------------------
% 0.55/0.52 % User time : 0.091 s
% 0.55/0.52 % System time : 0.015 s
% 0.55/0.52 % Total time : 0.107 s
% 0.55/0.52 % Maximum resident set size: 4608 pages
% 0.55/0.52 % E exiting
%------------------------------------------------------------------------------