%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU692^2 : 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 : n016.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 08:25:14 AM UTC 2026
% Result : Theorem 0.13s 0.23s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 22 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 332 ( 22 ~; 19 |; 6 &; 255 @)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
func: $i > $i > $i > $o ).
thf(decl_25,type,
funcSet: $i > $i > $i ).
thf(decl_26,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_27,type,
infuncsetfunc: $o ).
thf(decl_28,type,
funcext: $o ).
thf(decl_29,type,
esk1_4: $i > $i > $i > $i > $i ).
thf(decl_30,type,
esk2_0: $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(decl_32,type,
esk4_0: $i ).
thf(decl_33,type,
esk5_0: $i ).
thf(funcext2,conjecture,
( infuncsetfunc
=> ( funcext
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( funcSet @ X1 @ X2 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( ap @ X1 @ X2 @ X3 @ X5 )
= ( ap @ X1 @ X2 @ X4 @ X5 ) ) )
=> ( X3 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.frOFMAIgyF/E---3.1_416402.p',funcext2) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ( func @ X1 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.frOFMAIgyF/E---3.1_416402.p',infuncsetfunc) ).
thf(funcext,axiom,
( funcext
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( func @ X1 @ X2 @ X3 )
=> ! [X4: $i] :
( ( func @ X1 @ X2 @ X4 )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( ap @ X1 @ X2 @ X3 @ X5 )
= ( ap @ X1 @ X2 @ X4 @ X5 ) ) )
=> ( X3 = X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.frOFMAIgyF/E---3.1_416402.p',funcext) ).
thf(c_0_3,negated_conjecture,
~ ( infuncsetfunc
=> ( funcext
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( funcSet @ X1 @ X2 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( ap @ X1 @ X2 @ X3 @ X5 )
= ( ap @ X1 @ X2 @ X4 @ X5 ) ) )
=> ( X3 = X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcext2]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X19: $i,X20: $i,X21: $i] :
( ( in @ X21 @ ( funcSet @ X19 @ X20 ) )
=> ( func @ X19 @ X20 @ X21 ) )
=> ( ! [X22: $i,X23: $i,X24: $i] :
( ( func @ X22 @ X23 @ X24 )
=> ! [X25: $i] :
( ( func @ X22 @ X23 @ X25 )
=> ( ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ( ( ap @ X22 @ X23 @ X24 @ X26 )
= ( ap @ X22 @ X23 @ X25 @ X26 ) ) )
=> ( X24 = X25 ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( funcSet @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( funcSet @ X1 @ X2 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( ap @ X1 @ X2 @ X3 @ X5 )
= ( ap @ X1 @ X2 @ X4 @ X5 ) ) )
=> ( X3 = X4 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,infuncsetfunc]),funcext]) ).
thf(c_0_5,negated_conjecture,
! [X27: $i,X28: $i,X29: $i,X30: $i,X31: $i,X32: $i,X33: $i,X39: $i] :
( ( ~ ( in @ X29 @ ( funcSet @ X27 @ X28 ) )
| ( func @ X27 @ X28 @ X29 ) )
& ( ( in @ ( esk1_4 @ X30 @ X31 @ X32 @ X33 ) @ X30 )
| ( X32 = X33 )
| ~ ( func @ X30 @ X31 @ X33 )
| ~ ( func @ X30 @ X31 @ X32 ) )
& ( ( ( ap @ X30 @ X31 @ X32 @ ( esk1_4 @ X30 @ X31 @ X32 @ X33 ) )
!= ( ap @ X30 @ X31 @ X33 @ ( esk1_4 @ X30 @ X31 @ X32 @ X33 ) ) )
| ( X32 = X33 )
| ~ ( func @ X30 @ X31 @ X33 )
| ~ ( func @ X30 @ X31 @ X32 ) )
& ( in @ esk4_0 @ ( funcSet @ esk2_0 @ esk3_0 ) )
& ( in @ esk5_0 @ ( funcSet @ esk2_0 @ esk3_0 ) )
& ( ~ ( in @ X39 @ esk2_0 )
| ( ( ap @ esk2_0 @ esk3_0 @ esk4_0 @ X39 )
= ( ap @ esk2_0 @ esk3_0 @ esk5_0 @ X39 ) ) )
& ( esk4_0 != esk5_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_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( func @ X2 @ X3 @ X1 )
| ~ ( in @ X1 @ ( funcSet @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
in @ esk4_0 @ ( funcSet @ esk2_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( X3 = X4 )
| ( ( ap @ X1 @ X2 @ X3 @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) )
!= ( ap @ X1 @ X2 @ X4 @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) ) )
| ~ ( func @ X1 @ X2 @ X4 )
| ~ ( func @ X1 @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk2_0 @ esk3_0 @ esk4_0 @ X1 )
= ( ap @ esk2_0 @ esk3_0 @ esk5_0 @ X1 ) )
| ~ ( in @ X1 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
func @ esk2_0 @ esk3_0 @ esk4_0,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_11,negated_conjecture,
in @ esk5_0 @ ( funcSet @ esk2_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( X1 = esk4_0 )
| ( ( ap @ esk2_0 @ esk3_0 @ X1 @ ( esk1_4 @ esk2_0 @ esk3_0 @ X1 @ esk4_0 ) )
!= ( ap @ esk2_0 @ esk3_0 @ esk5_0 @ ( esk1_4 @ esk2_0 @ esk3_0 @ X1 @ esk4_0 ) ) )
| ~ ( in @ ( esk1_4 @ esk2_0 @ esk3_0 @ X1 @ esk4_0 ) @ esk2_0 )
| ~ ( func @ esk2_0 @ esk3_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
thf(c_0_13,negated_conjecture,
func @ esk2_0 @ esk3_0 @ esk5_0,
inference(spm,[status(thm)],[c_0_6,c_0_11]) ).
thf(c_0_14,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_15,negated_conjecture,
~ ( in @ ( esk1_4 @ esk2_0 @ esk3_0 @ esk5_0 @ esk4_0 ) @ esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13])]),c_0_14]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ( X3 = X4 )
| ~ ( func @ X1 @ X2 @ X4 )
| ~ ( func @ X1 @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_10]),c_0_13])]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU692^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.16 % Computer : n016.cluster.edu
% 0.13/0.16 % Model : x86_64 x86_64
% 0.13/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.16 % Memory : 8046.5625MB
% 0.13/0.16 % OS : Linux 6.8.0-71-generic
% 0.13/0.16 % CPULimit : 300
% 0.13/0.16 % WCLimit : 300
% 0.13/0.16 % DateTime : Tue Sep 29 14:16:22 UTC 2026
% 0.13/0.16 % CPUTime :
% 0.13/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.20 Running higher-order theorem proving
% 0.13/0.21 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.frOFMAIgyF/E---3.1_416402.p
% 0.13/0.23 % Version: 3.5.1-ho
% 0.13/0.23 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.13/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.23 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.13/0.23 % Starting post_as_ho8 with 300s (1) cores
% 0.13/0.23 % Starting post_as_ho3 with 300s (1) cores
% 0.13/0.23 % Starting post_as_ho2 with 300s (1) cores
% 0.13/0.23 % post_as_ho8 with pid 416416 completed with status 0
% 0.13/0.23 % Result found by post_as_ho8
% 0.13/0.23 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.13/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.23 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.13/0.23 % Starting post_as_ho8 with 300s (1) cores
% 0.13/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.13/0.23 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.13/0.23 % Search class: HGUSF-FFSF33-SFFFMFNN
% 0.13/0.23 % partial match(1): HGUSF-FFSF32-SFFFMFNN
% 0.13/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.23 % SubtermCWHack with pid 416419 completed with status 0
% 0.13/0.23 % Result found by SubtermCWHack
% 0.13/0.23 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.13/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.23 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.13/0.23 % Starting post_as_ho8 with 300s (1) cores
% 0.13/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.13/0.23 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.13/0.23 % Search class: HGUSF-FFSF33-SFFFMFNN
% 0.13/0.23 % partial match(1): HGUSF-FFSF32-SFFFMFNN
% 0.13/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.23 % Preprocessing time : 0.001 s
% 0.13/0.23
% 0.13/0.23 % Proof found!
% 0.13/0.23 % SZS status Theorem
% 0.13/0.23 % SZS output start CNFRefutation
% See solution above
% 0.13/0.23 % Parsed axioms : 9
% 0.13/0.23 % Removed by relevancy pruning/SinE : 6
% 0.13/0.23 % Initial clauses : 7
% 0.13/0.23 % Removed in clause preprocessing : 0
% 0.13/0.23 % Initial clauses in saturation : 7
% 0.13/0.23 % Processed clauses : 12
% 0.13/0.23 % ...of these trivial : 0
% 0.13/0.23 % ...subsumed : 0
% 0.13/0.23 % ...remaining for further processing : 12
% 0.13/0.23 % Other redundant clauses eliminated : 0
% 0.13/0.23 % Clauses deleted for lack of memory : 0
% 0.13/0.23 % Backward-subsumed : 0
% 0.13/0.23 % Backward-rewritten : 0
% 0.13/0.23 % Generated clauses : 8
% 0.13/0.23 % ...of the previous two non-redundant : 6
% 0.13/0.23 % ...aggressively subsumed : 0
% 0.13/0.23 % Contextual simplify-reflections : 0
% 0.13/0.23 % Paramodulations : 6
% 0.13/0.23 % Factorizations : 0
% 0.13/0.23 % NegExts : 0
% 0.13/0.23 % Equation resolutions : 2
% 0.13/0.23 % Disequality decompositions : 0
% 0.13/0.23 % Total rewrite steps : 5
% 0.13/0.23 % ...of those cached : 3
% 0.13/0.23 % Propositional unsat checks : 0
% 0.13/0.23 % Propositional check models : 0
% 0.13/0.23 % Propositional check unsatisfiable : 0
% 0.13/0.23 % Propositional clauses : 0
% 0.13/0.23 % Propositional clauses after purity: 0
% 0.13/0.23 % Propositional unsat core size : 0
% 0.13/0.23 % Propositional preprocessing time : 0.000
% 0.13/0.23 % Propositional encoding time : 0.000
% 0.13/0.23 % Propositional solver time : 0.000
% 0.13/0.23 % Success case prop preproc time : 0.000
% 0.13/0.23 % Success case prop encoding time : 0.000
% 0.13/0.23 % Success case prop solver time : 0.000
% 0.13/0.23 % Current number of processed clauses : 12
% 0.13/0.23 % Positive orientable unit clauses : 4
% 0.13/0.23 % Positive unorientable unit clauses: 0
% 0.13/0.23 % Negative unit clauses : 2
% 0.13/0.23 % Non-unit-clauses : 6
% 0.13/0.23 % Current number of unprocessed clauses: 1
% 0.13/0.23 % ...number of literals in the above : 4
% 0.13/0.23 % Current number of archived formulas : 0
% 0.13/0.23 % Current number of archived clauses : 0
% 0.13/0.23 % Clause-clause subsumption calls (NU) : 2
% 0.13/0.23 % Rec. Clause-clause subsumption calls : 2
% 0.13/0.23 % Non-unit clause-clause subsumptions : 0
% 0.13/0.23 % Unit Clause-clause subsumption calls : 1
% 0.13/0.23 % Rewrite failures with RHS unbound : 0
% 0.13/0.23 % BW rewrite match attempts : 1
% 0.13/0.23 % BW rewrite match successes : 0
% 0.13/0.23 % Condensation attempts : 0
% 0.13/0.23 % Condensation successes : 0
% 0.13/0.23 % Termbank termtop insertions : 1075
% 0.13/0.23 % Search garbage collected termcells : 340
% 0.13/0.23
% 0.13/0.23 % -------------------------------------------------
% 0.13/0.23 % User time : 0.006 s
% 0.13/0.23 % System time : 0.001 s
% 0.13/0.23 % Total time : 0.006 s
% 0.13/0.23 % Maximum resident set size: 3632 pages
% 0.13/0.23
% 0.13/0.23 % -------------------------------------------------
% 0.13/0.23 % User time : 0.008 s
% 0.13/0.23 % System time : 0.005 s
% 0.13/0.23 % Total time : 0.013 s
% 0.13/0.23 % Maximum resident set size: 4608 pages
% 0.13/0.23 % E exiting
%------------------------------------------------------------------------------