%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU169+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 : n008.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 02:24:06 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 81 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 87 ( 31 ~; 28 |; 12 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 1 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(l3_subset_1,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
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(c_0_5,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_6,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
inference(assume_negation,[status(cth)],[l3_subset_1]) ).
fof(c_0_7,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_8,plain,
! [X27,X28,X29,X30,X31,X32] :
( ( X32 = powerset(X31)
| subset(esk8_2(X31,X32),X31)
| in(esk8_2(X31,X32),X32) )
& ( X32 = powerset(X31)
| ~ subset(esk8_2(X31,X32),X31)
| ~ in(esk8_2(X31,X32),X32) )
& ( X28 != powerset(X27)
| in(X30,X28)
| ~ subset(X30,X27) )
& ( X28 != powerset(X27)
| subset(X29,X27)
| ~ in(X29,X28) ) ),
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)],[d1_zfmisc_1])])])])])])]) ).
fof(c_0_9,plain,
! [X21,X22] :
( ( ~ empty(X21)
| element(X22,X21)
| ~ empty(X22) )
& ( ~ empty(X21)
| empty(X22)
| ~ element(X22,X21) )
& ( empty(X21)
| element(X22,X21)
| ~ in(X22,X21) )
& ( empty(X21)
| in(X22,X21)
| ~ element(X22,X21) ) ),
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_10,negated_conjecture,
( ~ in(esk3_0,esk1_0)
& in(esk3_0,esk2_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_6])])])]) ).
fof(c_0_11,plain,
! [X34] : ~ empty(powerset(X34)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,plain,
( X2 != powerset(X3)
| ~ in(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X12,X13,X14,X15,X16] :
( ( subset(X15,X16)
| ~ in(esk4_2(X15,X16),X16) )
& ( subset(X15,X16)
| in(esk4_2(X15,X16),X15) )
& ( in(X14,X13)
| ~ in(X14,X12)
| ~ subset(X12,X13) ) ),
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])])])])])])]) ).
cnf(c_0_17,plain,
( ~ in(X1,powerset(X2))
| subset(X1,X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
in(esk2_0,powerset(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
subset(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ in(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(X1,esk2_0)
| in(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
in(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:55:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % new_bool_3 with pid 291022 completed with status 0
% 0.10/0.44 % Result found by new_bool_3
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 291043 completed with status 0
% 0.10/0.44 % Result found by SubtermCWHack
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 105
% 0.10/0.44 % Removed by relevancy pruning/SinE : 42
% 0.10/0.44 % Initial clauses : 107
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 107
% 0.10/0.44 % Processed clauses : 265
% 0.10/0.44 % ...of these trivial : 5
% 0.10/0.44 % ...subsumed : 122
% 0.10/0.44 % ...remaining for further processing : 138
% 0.10/0.44 % Other redundant clauses eliminated : 15
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 1
% 0.10/0.44 % Backward-rewritten : 1
% 0.10/0.44 % Generated clauses : 481
% 0.10/0.44 % ...of the previous two non-redundant : 311
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 1
% 0.10/0.44 % Paramodulations : 467
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 15
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 169
% 0.10/0.44 % ...of those cached : 131
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 125
% 0.10/0.44 % Positive orientable unit clauses : 35
% 0.10/0.44 % Positive unorientable unit clauses: 2
% 0.10/0.44 % Negative unit clauses : 25
% 0.10/0.44 % Non-unit-clauses : 63
% 0.10/0.44 % Current number of unprocessed clauses: 153
% 0.10/0.44 % ...number of literals in the above : 350
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 2
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 430
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 364
% 0.10/0.44 % Non-unit clause-clause subsumptions : 57
% 0.10/0.44 % Unit Clause-clause subsumption calls : 190
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 28
% 0.10/0.44 % BW rewrite match successes : 17
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 9610
% 0.10/0.44 % Search garbage collected termcells : 1678
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.011 s
% 0.10/0.44 % System time : 0.006 s
% 0.10/0.44 % Total time : 0.017 s
% 0.10/0.44 % Maximum resident set size: 3928 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.015 s
% 0.10/0.44 % System time : 0.010 s
% 0.10/0.44 % Total time : 0.024 s
% 0.10/0.44 % Maximum resident set size: 4864 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------