%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU625^2 : 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 : n007.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 08:24:46 AM UTC 2026
% Result : Theorem 0.26s 0.33s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 11 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 329 ( 20 ~; 23 |; 8 &; 242 @)
% ( 5 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 79 ( 0 ^; 79 !; 0 ?; 79 :)
% 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,
subset: $i > $i > $o ).
thf(decl_27,type,
subsetI2: $o ).
thf(decl_28,type,
subsetE: $o ).
thf(decl_29,type,
binunion: $i > $i > $i ).
thf(decl_30,type,
binunionLsub: $o ).
thf(decl_31,type,
binunionRsub: $o ).
thf(decl_32,type,
upairset2E: $o ).
thf(decl_33,type,
esk1_2: $i > $i > $i ).
thf(decl_34,type,
esk2_0: $i ).
thf(decl_35,type,
esk3_0: $i ).
thf(decl_36,type,
esk4_0: $i ).
thf(decl_37,type,
esk5_0: $i ).
thf(upairsubunion,conjecture,
( subsetI2
=> ( subsetE
=> ( binunionLsub
=> ( binunionRsub
=> ( upairset2E
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TtrXDgwI1d/E---3.1_3408196.p',upairsubunion) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TtrXDgwI1d/E---3.1_3408196.p',subsetI2) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TtrXDgwI1d/E---3.1_3408196.p',subsetE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TtrXDgwI1d/E---3.1_3408196.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TtrXDgwI1d/E---3.1_3408196.p',binunionRsub) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( in @ X5 @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) )
=> ( ( X5 = X3 )
| ( X5 = X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TtrXDgwI1d/E---3.1_3408196.p',upairset2E) ).
thf(c_0_6,negated_conjecture,
~ ( subsetI2
=> ( subsetE
=> ( binunionLsub
=> ( binunionRsub
=> ( upairset2E
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[upairsubunion]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X23: $i,X24: $i] :
( ! [X25: $i] :
( ( in @ X25 @ X23 )
=> ( in @ X25 @ X24 ) )
=> ( subset @ X23 @ X24 ) )
=> ( ! [X26: $i,X27: $i,X28: $i] :
( ( subset @ X26 @ X27 )
=> ( ( in @ X28 @ X26 )
=> ( in @ X28 @ X27 ) ) )
=> ( ! [X29: $i,X30: $i] : ( subset @ X29 @ ( binunion @ X29 @ X30 ) )
=> ( ! [X31: $i,X32: $i] : ( subset @ X32 @ ( binunion @ X31 @ X32 ) )
=> ( ! [X33: $i,X34: $i,X35: $i] :
( ( in @ X35 @ ( setadjoin @ X33 @ ( setadjoin @ X34 @ emptyset ) ) )
=> ( ( X35 = X33 )
| ( X35 = X34 ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,subsetI2]),subsetE]),binunionLsub]),binunionRsub]),upairset2E]) ).
thf(c_0_8,negated_conjecture,
! [X36: $i,X37: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i] :
( ( ( in @ ( esk1_2 @ X36 @ X37 ) @ X36 )
| ( subset @ X36 @ X37 ) )
& ( ~ ( in @ ( esk1_2 @ X36 @ X37 ) @ X37 )
| ( subset @ X36 @ X37 ) )
& ( ~ ( subset @ X39 @ X40 )
| ~ ( in @ X41 @ X39 )
| ( in @ X41 @ X40 ) )
& ( subset @ X42 @ ( binunion @ X42 @ X43 ) )
& ( subset @ X45 @ ( binunion @ X44 @ X45 ) )
& ( ~ ( in @ X48 @ ( setadjoin @ X46 @ ( setadjoin @ X47 @ emptyset ) ) )
| ( X48 = X46 )
| ( X48 = X47 ) )
& ( in @ esk4_0 @ esk2_0 )
& ( in @ esk5_0 @ esk3_0 )
& ~ ( subset @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ ( binunion @ esk2_0 @ esk3_0 ) ) ),
inference(distribute,[status(thm)],[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_7])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X1 = X3 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 )
| ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( ( esk1_2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
= X2 )
| ( ( esk1_2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
= X1 )
| ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( ( esk1_2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
= X2 )
| ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
| ~ ( in @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
~ ( subset @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ ( binunion @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( subset @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_18,negated_conjecture,
( ~ ( in @ esk5_0 @ ( binunion @ esk2_0 @ esk3_0 ) )
| ~ ( in @ esk4_0 @ ( binunion @ esk2_0 @ esk3_0 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
in @ esk4_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_21,negated_conjecture,
! [X2: $i,X1: $i] : ( subset @ X1 @ ( binunion @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_22,negated_conjecture,
~ ( in @ esk5_0 @ ( binunion @ esk2_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
| ~ ( in @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
thf(c_0_24,negated_conjecture,
in @ esk5_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU625^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n007.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 13:56:56 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.28 Running higher-order theorem proving
% 0.26/0.29 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.TtrXDgwI1d/E---3.1_3408196.p
% 0.26/0.33 % Version: 3.5.1-ho
% 0.26/0.33 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.26/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.33 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.26/0.33 % Starting post_as_ho8 with 300s (1) cores
% 0.26/0.33 % Starting post_as_ho3 with 300s (1) cores
% 0.26/0.33 % Starting post_as_ho2 with 300s (1) cores
% 0.26/0.33 % post_as_ho8 with pid 3408222 completed with status 0
% 0.26/0.33 % Result found by post_as_ho8
% 0.26/0.33 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.26/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.33 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.26/0.33 % Starting post_as_ho8 with 300s (1) cores
% 0.26/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.26/0.33 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.26/0.33 % Search class: HGUSS-FFSF22-SFFFMFNN
% 0.26/0.33 % partial match(1): HGUSF-FFSF22-SFFFMFNN
% 0.26/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.33 % SubtermCWHack with pid 3408227 completed with status 0
% 0.26/0.33 % Result found by SubtermCWHack
% 0.26/0.33 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.26/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.33 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.26/0.33 % Starting post_as_ho8 with 300s (1) cores
% 0.26/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.26/0.33 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.26/0.33 % Search class: HGUSS-FFSF22-SFFFMFNN
% 0.26/0.33 % partial match(1): HGUSF-FFSF22-SFFFMFNN
% 0.26/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.33 % Preprocessing time : 0.001 s
% 0.26/0.33
% 0.26/0.33 % Proof found!
% 0.26/0.33 % SZS status Theorem
% 0.26/0.33 % SZS output start CNFRefutation
% See solution above
% 0.26/0.33 % Parsed axioms : 16
% 0.26/0.33 % Removed by relevancy pruning/SinE : 10
% 0.26/0.33 % Initial clauses : 9
% 0.26/0.33 % Removed in clause preprocessing : 0
% 0.26/0.33 % Initial clauses in saturation : 9
% 0.26/0.33 % Processed clauses : 73
% 0.26/0.33 % ...of these trivial : 0
% 0.26/0.33 % ...subsumed : 13
% 0.26/0.33 % ...remaining for further processing : 60
% 0.26/0.33 % Other redundant clauses eliminated : 2
% 0.26/0.33 % Clauses deleted for lack of memory : 0
% 0.26/0.33 % Backward-subsumed : 1
% 0.26/0.33 % Backward-rewritten : 0
% 0.26/0.33 % Generated clauses : 192
% 0.26/0.33 % ...of the previous two non-redundant : 185
% 0.26/0.33 % ...aggressively subsumed : 0
% 0.26/0.33 % Contextual simplify-reflections : 0
% 0.26/0.33 % Paramodulations : 188
% 0.26/0.33 % Factorizations : 2
% 0.26/0.33 % NegExts : 0
% 0.26/0.33 % Equation resolutions : 2
% 0.26/0.33 % Disequality decompositions : 0
% 0.26/0.33 % Total rewrite steps : 4
% 0.26/0.33 % ...of those cached : 0
% 0.26/0.33 % Propositional unsat checks : 0
% 0.26/0.33 % Propositional check models : 0
% 0.26/0.33 % Propositional check unsatisfiable : 0
% 0.26/0.33 % Propositional clauses : 0
% 0.26/0.33 % Propositional clauses after purity: 0
% 0.26/0.33 % Propositional unsat core size : 0
% 0.26/0.33 % Propositional preprocessing time : 0.000
% 0.26/0.33 % Propositional encoding time : 0.000
% 0.26/0.33 % Propositional solver time : 0.000
% 0.26/0.33 % Success case prop preproc time : 0.000
% 0.26/0.33 % Success case prop encoding time : 0.000
% 0.26/0.33 % Success case prop solver time : 0.000
% 0.26/0.33 % Current number of processed clauses : 59
% 0.26/0.33 % Positive orientable unit clauses : 12
% 0.26/0.33 % Positive unorientable unit clauses: 0
% 0.26/0.33 % Negative unit clauses : 2
% 0.26/0.33 % Non-unit-clauses : 45
% 0.26/0.33 % Current number of unprocessed clauses: 120
% 0.26/0.33 % ...number of literals in the above : 284
% 0.26/0.33 % Current number of archived formulas : 0
% 0.26/0.33 % Current number of archived clauses : 1
% 0.26/0.33 % Clause-clause subsumption calls (NU) : 562
% 0.26/0.33 % Rec. Clause-clause subsumption calls : 524
% 0.26/0.33 % Non-unit clause-clause subsumptions : 13
% 0.26/0.33 % Unit Clause-clause subsumption calls : 21
% 0.26/0.33 % Rewrite failures with RHS unbound : 0
% 0.26/0.33 % BW rewrite match attempts : 25
% 0.26/0.33 % BW rewrite match successes : 0
% 0.26/0.33 % Condensation attempts : 0
% 0.26/0.33 % Condensation successes : 0
% 0.26/0.33 % Termbank termtop insertions : 4402
% 0.26/0.33 % Search garbage collected termcells : 392
% 0.26/0.33
% 0.26/0.33 % -------------------------------------------------
% 0.26/0.33 % User time : 0.011 s
% 0.26/0.33 % System time : 0.001 s
% 0.26/0.33 % Total time : 0.012 s
% 0.26/0.33 % Maximum resident set size: 3640 pages
% 0.26/0.33
% 0.26/0.33 % -------------------------------------------------
% 0.26/0.33 % User time : 0.012 s
% 0.26/0.33 % System time : 0.005 s
% 0.26/0.33 % Total time : 0.018 s
% 0.26/0.33 % Maximum resident set size: 4608 pages
% 0.26/0.33 % E exiting
%------------------------------------------------------------------------------