%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU802^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:25:41 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 16 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 243 ( 15 ~; 10 |; 10 &; 190 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 72 ( 18 ^; 47 !; 7 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
dsetconstrER: $o ).
thf(decl_26,type,
funcSet: $i > $i > $i ).
thf(decl_27,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_28,type,
surjective: $i > $i > $i > $o ).
thf(decl_29,type,
surjFuncSet: $i > $i > $i ).
thf(decl_30,type,
esk1_0: $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(decl_34,type,
esk5_4: $i > $i > $i > $i > $i ).
thf(surjFuncSetFuncSurj,conjecture,
( dsetconstrER
=> ! [X3: $i,X4: $i,X6: $i] :
( ( in @ X6 @ ( surjFuncSet @ X3 @ X4 ) )
=> ( surjective @ X3 @ X4 @ X6 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.twOKKs3bRG/E---3.1_807045.p',surjFuncSetFuncSurj) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.twOKKs3bRG/E---3.1_807045.p',dsetconstrER) ).
thf(surjective,axiom,
( surjective
= ( ^ [X1: $i,X5: $i,X6: $i] :
! [X3: $i] :
( ( in @ X3 @ X5 )
=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( ( ap @ X1 @ X5 @ X6 @ X4 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.twOKKs3bRG/E---3.1_807045.p',surjective) ).
thf(surjFuncSet,axiom,
( surjFuncSet
= ( ^ [X1: $i,X5: $i] :
( dsetconstr @ ( funcSet @ X1 @ X5 )
@ ^ [X6: $i] : ( surjective @ X1 @ X5 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.twOKKs3bRG/E---3.1_807045.p',surjFuncSet) ).
thf(c_0_4,negated_conjecture,
~ ( dsetconstrER
=> ! [X3: $i,X4: $i,X6: $i] :
( ( in @ X6 @ ( surjFuncSet @ X3 @ X4 ) )
=> ( surjective @ X3 @ X4 @ X6 ) ) ),
inference(assume_negation,[status(cth)],[surjFuncSetFuncSurj]) ).
thf(c_0_5,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_6,plain,
( surjective
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
! [X3: $i] :
( ( in @ X3 @ Z1 )
=> ? [X4: $i] :
( ( in @ X4 @ Z0 )
& ( ( ap @ Z0 @ Z1 @ Z2 @ X4 )
= X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[surjective]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X15: $i,X16: $i > $o,X17: $i] :
( ( in @ X17 @ ( dsetconstr @ X15 @ X16 ) )
=> ( X16 @ X17 ) )
=> ! [X3: $i,X4: $i,X6: $i] :
( ( in @ X6 @ ( surjFuncSet @ X3 @ X4 ) )
=> ! [X18: $i] :
( ( in @ X18 @ X4 )
=> ? [X19: $i] :
( ( in @ X19 @ X3 )
& ( ( ap @ X3 @ X4 @ X6 @ X19 )
= X18 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6])]) ).
thf(c_0_8,plain,
( surjFuncSet
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( funcSet @ Z0 @ Z1 )
@ ^ [Z2: $i] :
! [X13: $i] :
( ( in @ X13 @ Z1 )
=> ? [X14: $i] :
( ( in @ X14 @ Z0 )
& ( ( ap @ Z0 @ Z1 @ Z2 @ X14 )
= X13 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[surjFuncSet]),c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X20: $i,X21: $i > $o,X22: $i,X27: $i] :
( ( ~ ( in @ X22 @ ( dsetconstr @ X20 @ X21 ) )
| ( X21 @ X22 ) )
& ( in @ esk3_0 @ ( surjFuncSet @ esk1_0 @ esk2_0 ) )
& ( in @ esk4_0 @ esk2_0 )
& ( ~ ( in @ X27 @ esk1_0 )
| ( ( ap @ esk1_0 @ esk2_0 @ esk3_0 @ X27 )
!= esk4_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_7])])])])]) ).
thf(c_0_10,plain,
( surjFuncSet
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( funcSet @ Z0 @ Z1 )
@ ^ [Z2: $i] :
! [X38: $i] :
( ( in @ X38 @ Z1 )
=> ? [X39: $i] :
( ( in @ X39 @ Z0 )
& ( ( ap @ Z0 @ Z1 @ Z2 @ X39 )
= X38 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X1: $i,X3: $i] :
( ( dsetconstr @ ( funcSet @ X1 @ X3 )
@ ^ [Z0: $i] :
! [X40: $i] :
( ( in @ X40 @ X3 )
=> ? [X41: $i] :
( ( in @ X41 @ X1 )
& ( ( ap @ X1 @ X3 @ Z0 @ X41 )
= X40 ) ) ) )
= ( surjFuncSet @ X1 @ X3 ) ),
inference(arg_cong,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X4: $i,X3: $i,X1: $i] :
( ! [X42: $i] :
( ( in @ X42 @ X1 )
=> ? [X43: $i] :
( ( in @ X43 @ X3 )
& ( ( ap @ X3 @ X1 @ X4 @ X43 )
= X42 ) ) )
| ~ ( in @ X4 @ ( surjFuncSet @ X3 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk1_0 )
| ( ( ap @ esk1_0 @ esk2_0 @ esk3_0 @ X1 )
!= esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X3: $i] :
( ( ( ap @ X1 @ X3 @ X4 @ ( esk5_4 @ X4 @ X1 @ X3 @ X5 ) )
= X5 )
| ~ ( in @ X4 @ ( surjFuncSet @ X1 @ X3 ) )
| ~ ( in @ X5 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
in @ esk3_0 @ ( surjFuncSet @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,negated_conjecture,
in @ esk4_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X3: $i,X5: $i,X4: $i] :
( ( in @ ( esk5_4 @ X1 @ X3 @ X4 @ X5 ) @ X3 )
| ~ ( in @ X1 @ ( surjFuncSet @ X3 @ X4 ) )
| ~ ( in @ X5 @ X4 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_13]) ).
thf(c_0_19,negated_conjecture,
~ ( in @ ( esk5_4 @ esk3_0 @ esk1_0 @ esk2_0 @ esk4_0 ) @ esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])])]),c_0_17])]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk5_4 @ esk3_0 @ esk1_0 @ esk2_0 @ X1 ) @ esk1_0 )
| ~ ( in @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU802^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.15 % Computer : n006.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Sep 29 14:31:54 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 Running higher-order theorem proving
% 0.09/0.20 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.twOKKs3bRG/E---3.1_807045.p
% 0.09/0.23 % Version: 3.5.1-ho
% 0.09/0.23 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.23 % Starting sh4l with 300s (1) cores
% 0.09/0.23 % Starting lpo8_s with 300s (1) cores
% 0.09/0.23 % sh4l with pid 807060 completed with status 0
% 0.09/0.23 % Result found by sh4l
% 0.09/0.23 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.23 % Starting sh4l with 300s (1) cores
% 0.09/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.23 % No SInE strategy applied
% 0.09/0.23 % Search class: HHHSF-FFSS32-DSFFMSBN
% 0.09/0.23 % partial match(2): HHUSF-FFSS32-SSFFMSBN
% 0.09/0.23 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.23 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.23 % SubtermCWHack with pid 807062 completed with status 0
% 0.09/0.23 % Result found by SubtermCWHack
% 0.09/0.23 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.23 % Starting sh4l with 300s (1) cores
% 0.09/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.23 % No SInE strategy applied
% 0.09/0.23 % Search class: HHHSF-FFSS32-DSFFMSBN
% 0.09/0.23 % partial match(2): HHUSF-FFSS32-SSFFMSBN
% 0.09/0.23 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.23 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.23 % Preprocessing time : 0.001 s
% 0.09/0.23
% 0.09/0.23 % Proof found!
% 0.09/0.23 % SZS status Theorem
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23 % Parsed axioms : 11
% 0.09/0.23 % Removed by relevancy pruning/SinE : 0
% 0.09/0.23 % Initial clauses : 12
% 0.09/0.23 % Removed in clause preprocessing : 7
% 0.09/0.23 % Initial clauses in saturation : 5
% 0.09/0.23 % Processed clauses : 13
% 0.09/0.23 % ...of these trivial : 1
% 0.09/0.23 % ...subsumed : 0
% 0.09/0.23 % ...remaining for further processing : 12
% 0.09/0.23 % Other redundant clauses eliminated : 1
% 0.09/0.23 % Clauses deleted for lack of memory : 0
% 0.09/0.23 % Backward-subsumed : 0
% 0.09/0.23 % Backward-rewritten : 0
% 0.09/0.23 % Generated clauses : 10
% 0.09/0.23 % ...of the previous two non-redundant : 8
% 0.09/0.23 % ...aggressively subsumed : 0
% 0.09/0.23 % Contextual simplify-reflections : 0
% 0.09/0.23 % Paramodulations : 4
% 0.09/0.23 % Factorizations : 0
% 0.09/0.23 % NegExts : 0
% 0.09/0.23 % Equation resolutions : 1
% 0.09/0.23 % Disequality decompositions : 0
% 0.09/0.23 % Total rewrite steps : 4
% 0.09/0.23 % ...of those cached : 1
% 0.09/0.23 % Propositional unsat checks : 0
% 0.09/0.23 % Propositional check models : 0
% 0.09/0.23 % Propositional check unsatisfiable : 0
% 0.09/0.23 % Propositional clauses : 0
% 0.09/0.23 % Propositional clauses after purity: 0
% 0.09/0.23 % Propositional unsat core size : 0
% 0.09/0.23 % Propositional preprocessing time : 0.000
% 0.09/0.23 % Propositional encoding time : 0.000
% 0.09/0.23 % Propositional solver time : 0.000
% 0.09/0.23 % Success case prop preproc time : 0.000
% 0.09/0.23 % Success case prop encoding time : 0.000
% 0.09/0.23 % Success case prop solver time : 0.000
% 0.09/0.23 % Current number of processed clauses : 11
% 0.09/0.23 % Positive orientable unit clauses : 5
% 0.09/0.23 % Positive unorientable unit clauses: 0
% 0.09/0.23 % Negative unit clauses : 1
% 0.09/0.23 % Non-unit-clauses : 5
% 0.09/0.23 % Current number of unprocessed clauses: 0
% 0.09/0.23 % ...number of literals in the above : 0
% 0.09/0.23 % Current number of archived formulas : 0
% 0.09/0.23 % Current number of archived clauses : 1
% 0.09/0.23 % Clause-clause subsumption calls (NU) : 8
% 0.09/0.23 % Rec. Clause-clause subsumption calls : 8
% 0.09/0.23 % Non-unit clause-clause subsumptions : 0
% 0.09/0.23 % Unit Clause-clause subsumption calls : 1
% 0.09/0.23 % Rewrite failures with RHS unbound : 0
% 0.09/0.23 % BW rewrite match attempts : 1
% 0.09/0.23 % BW rewrite match successes : 0
% 0.09/0.23 % Condensation attempts : 0
% 0.09/0.23 % Condensation successes : 0
% 0.09/0.23 % Termbank termtop insertions : 1249
% 0.09/0.23 % Search garbage collected termcells : 236
% 0.09/0.23
% 0.09/0.23 % -------------------------------------------------
% 0.09/0.23 % User time : 0.003 s
% 0.09/0.23 % System time : 0.001 s
% 0.09/0.23 % Total time : 0.004 s
% 0.09/0.23 % Maximum resident set size: 3640 pages
% 0.09/0.23
% 0.09/0.23 % -------------------------------------------------
% 0.09/0.23 % User time : 0.004 s
% 0.09/0.23 % System time : 0.006 s
% 0.09/0.23 % Total time : 0.010 s
% 0.09/0.23 % Maximum resident set size: 4864 pages
% 0.09/0.23 % E exiting
%------------------------------------------------------------------------------