%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU735^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 : Wed Sep 30 08:27:35 AM UTC 2026
% Result : Theorem 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 210 ( 12 ~; 8 |; 4 &; 166 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
subset: $i > $i > $o ).
thf(decl_26,type,
powersetI1: $o ).
thf(decl_27,type,
binintersect: $i > $i > $i ).
thf(decl_28,type,
setminus: $i > $i > $i ).
thf(decl_29,type,
complementSubsetComplementIntersect: $o ).
thf(decl_30,type,
esk1_0: $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(complementInPowersetComplementIntersect,conjecture,
( powersetI1
=> ( complementSubsetComplementIntersect
=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X3 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BcHCLUX1Rc/E---3.1_843677.p',complementInPowersetComplementIntersect) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ X1 )
=> ( in @ X2 @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BcHCLUX1Rc/E---3.1_843677.p',powersetI1) ).
thf(complementSubsetComplementIntersect,axiom,
( complementSubsetComplementIntersect
<=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BcHCLUX1Rc/E---3.1_843677.p',complementSubsetComplementIntersect) ).
thf(c_0_3,negated_conjecture,
~ ( powersetI1
=> ( complementSubsetComplementIntersect
=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X3 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[complementInPowersetComplementIntersect]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X13: $i,X14: $i] :
( ( subset @ X14 @ X13 )
=> ( in @ X14 @ ( powerset @ X13 ) ) )
=> ( ! [X15: $i,X16: $i] :
( ( in @ X16 @ ( powerset @ X15 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X15 ) )
=> ( subset @ ( setminus @ X15 @ X16 ) @ ( setminus @ X15 @ ( binintersect @ X16 @ X17 ) ) ) ) )
=> ! [X1: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X3 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,powersetI1]),complementSubsetComplementIntersect]) ).
thf(c_0_5,negated_conjecture,
! [X18: $i,X19: $i,X20: $i,X21: $i,X22: $i] :
( ( ~ ( subset @ X19 @ X18 )
| ( in @ X19 @ ( powerset @ X18 ) ) )
& ( ~ ( in @ X21 @ ( powerset @ X20 ) )
| ~ ( in @ X22 @ ( powerset @ X20 ) )
| ( subset @ ( setminus @ X20 @ X21 ) @ ( setminus @ X20 @ ( binintersect @ X21 @ X22 ) ) ) )
& ( in @ esk2_0 @ ( powerset @ esk1_0 ) )
& ( in @ esk3_0 @ ( powerset @ esk1_0 ) )
& ~ ( in @ ( setminus @ esk1_0 @ esk2_0 ) @ ( powerset @ ( setminus @ esk1_0 @ ( binintersect @ esk2_0 @ esk3_0 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( subset @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ( in @ ( setminus @ esk1_0 @ esk2_0 ) @ ( powerset @ ( setminus @ esk1_0 @ ( binintersect @ esk2_0 @ esk3_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) ) ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,negated_conjecture,
in @ esk3_0 @ ( powerset @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
in @ esk2_0 @ ( powerset @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU735^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n019.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 14:18:17 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.20 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.BcHCLUX1Rc/E---3.1_843677.p
% 0.10/0.22 % Version: 3.5.1-ho
% 0.10/0.22 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.10/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.22 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.10/0.22 % Starting post_as_ho8 with 300s (1) cores
% 0.10/0.22 % Starting post_as_ho3 with 300s (1) cores
% 0.10/0.22 % Starting post_as_ho2 with 300s (1) cores
% 0.10/0.22 % post_as_ho8 with pid 843691 completed with status 0
% 0.10/0.22 % Result found by post_as_ho8
% 0.10/0.22 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.10/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.22 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.10/0.22 % Starting post_as_ho8 with 300s (1) cores
% 0.10/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.10/0.22 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.10/0.22 % Search class: HHUNF-FFSF21-MFFFMFNN
% 0.10/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.22 % SubtermCWHack with pid 843695 completed with status 0
% 0.10/0.22 % Result found by SubtermCWHack
% 0.10/0.22 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.10/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.22 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.10/0.22 % Starting post_as_ho8 with 300s (1) cores
% 0.10/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.10/0.22 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.10/0.22 % Search class: HHUNF-FFSF21-MFFFMFNN
% 0.10/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.22 % Preprocessing time : 0.001 s
% 0.10/0.22
% 0.10/0.22 % Proof found!
% 0.10/0.22 % SZS status Theorem
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22 % Parsed axioms : 10
% 0.10/0.22 % Removed by relevancy pruning/SinE : 7
% 0.10/0.22 % Initial clauses : 5
% 0.10/0.22 % Removed in clause preprocessing : 0
% 0.10/0.22 % Initial clauses in saturation : 5
% 0.10/0.22 % Processed clauses : 6
% 0.10/0.22 % ...of these trivial : 0
% 0.10/0.22 % ...subsumed : 0
% 0.10/0.22 % ...remaining for further processing : 6
% 0.10/0.22 % Other redundant clauses eliminated : 0
% 0.10/0.22 % Clauses deleted for lack of memory : 0
% 0.10/0.22 % Backward-subsumed : 0
% 0.10/0.22 % Backward-rewritten : 0
% 0.10/0.22 % Generated clauses : 2
% 0.10/0.22 % ...of the previous two non-redundant : 1
% 0.10/0.22 % ...aggressively subsumed : 0
% 0.10/0.22 % Contextual simplify-reflections : 0
% 0.10/0.22 % Paramodulations : 2
% 0.10/0.22 % Factorizations : 0
% 0.10/0.22 % NegExts : 0
% 0.10/0.22 % Equation resolutions : 0
% 0.10/0.22 % Disequality decompositions : 0
% 0.10/0.22 % Total rewrite steps : 2
% 0.10/0.22 % ...of those cached : 0
% 0.10/0.22 % Propositional unsat checks : 0
% 0.10/0.22 % Propositional check models : 0
% 0.10/0.22 % Propositional check unsatisfiable : 0
% 0.10/0.22 % Propositional clauses : 0
% 0.10/0.22 % Propositional clauses after purity: 0
% 0.10/0.22 % Propositional unsat core size : 0
% 0.10/0.22 % Propositional preprocessing time : 0.000
% 0.10/0.22 % Propositional encoding time : 0.000
% 0.10/0.22 % Propositional solver time : 0.000
% 0.10/0.22 % Success case prop preproc time : 0.000
% 0.10/0.22 % Success case prop encoding time : 0.000
% 0.10/0.22 % Success case prop solver time : 0.000
% 0.10/0.22 % Current number of processed clauses : 6
% 0.10/0.22 % Positive orientable unit clauses : 2
% 0.10/0.22 % Positive unorientable unit clauses: 0
% 0.10/0.22 % Negative unit clauses : 1
% 0.10/0.22 % Non-unit-clauses : 3
% 0.10/0.22 % Current number of unprocessed clauses: 0
% 0.10/0.22 % ...number of literals in the above : 0
% 0.10/0.22 % Current number of archived formulas : 0
% 0.10/0.22 % Current number of archived clauses : 0
% 0.10/0.22 % Clause-clause subsumption calls (NU) : 5
% 0.10/0.22 % Rec. Clause-clause subsumption calls : 5
% 0.10/0.22 % Non-unit clause-clause subsumptions : 0
% 0.10/0.22 % Unit Clause-clause subsumption calls : 0
% 0.10/0.22 % Rewrite failures with RHS unbound : 0
% 0.10/0.22 % BW rewrite match attempts : 0
% 0.10/0.22 % BW rewrite match successes : 0
% 0.10/0.22 % Condensation attempts : 0
% 0.10/0.22 % Condensation successes : 0
% 0.10/0.22 % Termbank termtop insertions : 672
% 0.10/0.22 % Search garbage collected termcells : 209
% 0.10/0.22
% 0.10/0.22 % -------------------------------------------------
% 0.10/0.22 % User time : 0.003 s
% 0.10/0.22 % System time : 0.002 s
% 0.10/0.22 % Total time : 0.005 s
% 0.10/0.22 % Maximum resident set size: 3580 pages
% 0.10/0.22
% 0.10/0.22 % -------------------------------------------------
% 0.10/0.22 % User time : 0.004 s
% 0.10/0.22 % System time : 0.005 s
% 0.10/0.22 % Total time : 0.009 s
% 0.10/0.22 % Maximum resident set size: 4864 pages
% 0.10/0.22 % E exiting
%------------------------------------------------------------------------------