%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU638^2 : 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 : n001.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 08:24:49 AM UTC 2026
% Result : Theorem 0.14s 0.24s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 11 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 182 ( 10 ~; 6 |; 12 &; 135 @)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 19 ^; 38 !; 8 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
thf(decl_26,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_27,type,
dsetconstrEL: $o ).
thf(decl_28,type,
dsetconstrER: $o ).
thf(decl_29,type,
singleton: $i > $o ).
thf(decl_30,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_31,type,
esk1_0: $i ).
thf(decl_32,type,
epred1_0: $i > $o ).
thf(decl_33,type,
esk2_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.glduoyzZE4/E---3.1_1291814.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X1
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.glduoyzZE4/E---3.1_1291814.p',singleton) ).
thf(ex1E1,conjecture,
( dsetconstrEL
=> ( dsetconstrER
=> ! [X1: $i,X2: $i > $o] :
( ( ex1 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.glduoyzZE4/E---3.1_1291814.p',ex1E1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.glduoyzZE4/E---3.1_1291814.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.glduoyzZE4/E---3.1_1291814.p',dsetconstrEL) ).
thf(c_0_5,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X14: $i] :
( ( in @ X14
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X14 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_6,plain,
( singleton
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ( Z0
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_7,negated_conjecture,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ! [X1: $i,X2: $i > $o] :
( ( ex1 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[ex1E1]) ).
thf(c_0_8,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X14: $i] :
( ( in @ X14
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X14 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_9,plain,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_10,plain,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( in @ X3 @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_11,negated_conjecture,
~ ( ! [X15: $i,X16: $i > $o,X17: $i] :
( ( in @ X17 @ ( dsetconstr @ X15 @ X16 ) )
=> ( in @ X17 @ X15 ) )
=> ( ! [X18: $i,X19: $i > $o,X20: $i] :
( ( in @ X20 @ ( dsetconstr @ X18 @ X19 ) )
=> ( X19 @ X20 ) )
=> ! [X1: $i,X2: $i > $o] :
( ? [X21: $i] :
( ( in @ X21 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X21 @ emptyset ) ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ X3 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7]),c_0_8]),c_0_9]),c_0_10])]) ).
thf(c_0_12,negated_conjecture,
! [X22: $i,X23: $i > $o,X24: $i,X25: $i,X26: $i > $o,X27: $i,X31: $i] :
( ( ~ ( in @ X24 @ ( dsetconstr @ X22 @ X23 ) )
| ( in @ X24 @ X22 ) )
& ( ~ ( in @ X27 @ ( dsetconstr @ X25 @ X26 ) )
| ( X26 @ X27 ) )
& ( in @ esk2_0 @ ( dsetconstr @ esk1_0 @ epred1_0 ) )
& ( ( dsetconstr @ esk1_0 @ epred1_0 )
= ( setadjoin @ esk2_0 @ emptyset ) )
& ( ~ ( in @ X31 @ esk1_0 )
| ~ ( epred1_0 @ X31 ) ) ),
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_11])])])])]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
in @ esk2_0 @ ( dsetconstr @ esk1_0 @ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk1_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,negated_conjecture,
in @ esk2_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,negated_conjecture,
epred1_0 @ esk2_0,
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU638^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.16 % Computer : n001.cluster.edu
% 0.14/0.16 % Model : x86_64 x86_64
% 0.14/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.16 % Memory : 8046.5625MB
% 0.14/0.16 % OS : Linux 6.8.0-71-generic
% 0.14/0.16 % CPULimit : 300
% 0.14/0.16 % WCLimit : 300
% 0.14/0.16 % DateTime : Tue Sep 29 14:06:50 UTC 2026
% 0.14/0.16 % CPUTime :
% 0.14/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.21 Running higher-order theorem proving
% 0.14/0.22 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.glduoyzZE4/E---3.1_1291814.p
% 0.14/0.24 % Version: 3.5.1-ho
% 0.14/0.24 % Preprocessing class: HSSSSLSSSLMNHSA.
% 0.14/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.14/0.24 % Starting new_ho_7 with 300s (1) cores
% 0.14/0.24 % Starting lpo8_lambda_fix with 300s (1) cores
% 0.14/0.24 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.14/0.24 % lpo8_lambda_fix with pid 1291839 completed with status 0
% 0.14/0.24 % Result found by lpo8_lambda_fix
% 0.14/0.24 % Preprocessing class: HSSSSLSSSLMNHSA.
% 0.14/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.14/0.24 % Starting new_ho_7 with 300s (1) cores
% 0.14/0.24 % Starting lpo8_lambda_fix with 300s (1) cores
% 0.14/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,5.0,,4,20000,1.0))
% 0.14/0.24 % SinE strategy is GSinE(CountFormulas,,5.0,,4,20000,1.0)
% 0.14/0.24 % Search class: HHHSF-FFSF22-SHSFMSBN
% 0.14/0.24 % partial match(2): HHUSF-FFSF32-SHSFMSBN
% 0.14/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.24 % SubtermCWHack with pid 1291841 completed with status 0
% 0.14/0.24 % Result found by SubtermCWHack
% 0.14/0.24 % Preprocessing class: HSSSSLSSSLMNHSA.
% 0.14/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.14/0.24 % Starting new_ho_7 with 300s (1) cores
% 0.14/0.24 % Starting lpo8_lambda_fix with 300s (1) cores
% 0.14/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,5.0,,4,20000,1.0))
% 0.14/0.24 % SinE strategy is GSinE(CountFormulas,,5.0,,4,20000,1.0)
% 0.14/0.24 % Search class: HHHSF-FFSF22-SHSFMSBN
% 0.14/0.24 % partial match(2): HHUSF-FFSF32-SHSFMSBN
% 0.14/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.24 % Preprocessing time : 0.001 s
% 0.14/0.24
% 0.14/0.24 % Proof found!
% 0.14/0.24 % SZS status Theorem
% 0.14/0.24 % SZS output start CNFRefutation
% See solution above
% 0.14/0.24 % Parsed axioms : 13
% 0.14/0.24 % Removed by relevancy pruning/SinE : 8
% 0.14/0.24 % Initial clauses : 5
% 0.14/0.24 % Removed in clause preprocessing : 0
% 0.14/0.24 % Initial clauses in saturation : 5
% 0.14/0.24 % Processed clauses : 7
% 0.14/0.24 % ...of these trivial : 0
% 0.14/0.24 % ...subsumed : 0
% 0.14/0.24 % ...remaining for further processing : 7
% 0.14/0.24 % Other redundant clauses eliminated : 0
% 0.14/0.24 % Clauses deleted for lack of memory : 0
% 0.14/0.24 % Backward-subsumed : 0
% 0.14/0.24 % Backward-rewritten : 0
% 0.14/0.24 % Generated clauses : 3
% 0.14/0.24 % ...of the previous two non-redundant : 2
% 0.14/0.24 % ...aggressively subsumed : 0
% 0.14/0.24 % Contextual simplify-reflections : 0
% 0.14/0.24 % Paramodulations : 3
% 0.14/0.24 % Factorizations : 0
% 0.14/0.24 % NegExts : 0
% 0.14/0.24 % Equation resolutions : 0
% 0.14/0.24 % Disequality decompositions : 0
% 0.14/0.24 % Total rewrite steps : 1
% 0.14/0.24 % ...of those cached : 0
% 0.14/0.24 % Propositional unsat checks : 0
% 0.14/0.24 % Propositional check models : 0
% 0.14/0.24 % Propositional check unsatisfiable : 0
% 0.14/0.24 % Propositional clauses : 0
% 0.14/0.24 % Propositional clauses after purity: 0
% 0.14/0.24 % Propositional unsat core size : 0
% 0.14/0.24 % Propositional preprocessing time : 0.000
% 0.14/0.24 % Propositional encoding time : 0.000
% 0.14/0.24 % Propositional solver time : 0.000
% 0.14/0.24 % Success case prop preproc time : 0.000
% 0.14/0.24 % Success case prop encoding time : 0.000
% 0.14/0.24 % Success case prop solver time : 0.000
% 0.14/0.24 % Current number of processed clauses : 7
% 0.14/0.24 % Positive orientable unit clauses : 4
% 0.14/0.24 % Positive unorientable unit clauses: 0
% 0.14/0.24 % Negative unit clauses : 0
% 0.14/0.24 % Non-unit-clauses : 3
% 0.14/0.24 % Current number of unprocessed clauses: 0
% 0.14/0.24 % ...number of literals in the above : 0
% 0.14/0.24 % Current number of archived formulas : 0
% 0.14/0.24 % Current number of archived clauses : 0
% 0.14/0.24 % Clause-clause subsumption calls (NU) : 1
% 0.14/0.24 % Rec. Clause-clause subsumption calls : 1
% 0.14/0.24 % Non-unit clause-clause subsumptions : 0
% 0.14/0.24 % Unit Clause-clause subsumption calls : 0
% 0.14/0.24 % Rewrite failures with RHS unbound : 0
% 0.14/0.24 % BW rewrite match attempts : 0
% 0.14/0.24 % BW rewrite match successes : 0
% 0.14/0.24 % Condensation attempts : 0
% 0.14/0.24 % Condensation successes : 0
% 0.14/0.24 % Termbank termtop insertions : 865
% 0.14/0.24 % Search garbage collected termcells : 326
% 0.14/0.24
% 0.14/0.24 % -------------------------------------------------
% 0.14/0.24 % User time : 0.003 s
% 0.14/0.24 % System time : 0.002 s
% 0.14/0.24 % Total time : 0.005 s
% 0.14/0.24 % Maximum resident set size: 3584 pages
% 0.14/0.24
% 0.14/0.24 % -------------------------------------------------
% 0.14/0.24 % User time : 0.004 s
% 0.14/0.24 % System time : 0.007 s
% 0.14/0.24 % Total time : 0.011 s
% 0.14/0.24 % Maximum resident set size: 4864 pages
% 0.14/0.24 % E exiting
%------------------------------------------------------------------------------