%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU801^2 : 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 : n012.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 0.07s 0.19s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 12 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 184 ( 6 ~; 2 |; 9 &; 149 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 58 ( 20 ^; 31 !; 7 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
dsetconstrEL: $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(surjFuncSet,axiom,
( surjFuncSet
= ( ^ [X1: $i,X5: $i] :
( dsetconstr @ ( funcSet @ X1 @ X5 )
@ ^ [X6: $i] : ( surjective @ X1 @ X5 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KCB2vVDm0r/E---3.1_183459.p',surjFuncSet) ).
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.KCB2vVDm0r/E---3.1_183459.p',surjective) ).
thf(surjFuncSetFuncIn,conjecture,
( dsetconstrEL
=> ! [X1: $i,X5: $i,X6: $i] :
( ( in @ X6 @ ( surjFuncSet @ X1 @ X5 ) )
=> ( in @ X6 @ ( funcSet @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KCB2vVDm0r/E---3.1_183459.p',surjFuncSetFuncIn) ).
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/sandbox/tmp/tmp.KCB2vVDm0r/E---3.1_183459.p',dsetconstrEL) ).
thf(c_0_4,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(fof_simplification,[status(thm)],[surjFuncSet]) ).
thf(c_0_5,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_6,negated_conjecture,
~ ( dsetconstrEL
=> ! [X1: $i,X5: $i,X6: $i] :
( ( in @ X6 @ ( surjFuncSet @ X1 @ X5 ) )
=> ( in @ X6 @ ( funcSet @ X1 @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[surjFuncSetFuncIn]) ).
thf(c_0_7,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)],[c_0_4,c_0_5]) ).
thf(c_0_8,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_9,negated_conjecture,
~ ( ! [X15: $i,X16: $i > $o,X17: $i] :
( ( in @ X17 @ ( dsetconstr @ X15 @ X16 ) )
=> ( in @ X17 @ X15 ) )
=> ! [X1: $i,X5: $i,X6: $i] :
( ( in @ X6
@ ( dsetconstr @ ( funcSet @ X1 @ X5 )
@ ^ [Z0: $i] :
! [X18: $i] :
( ( in @ X18 @ X5 )
=> ? [X19: $i] :
( ( in @ X19 @ X1 )
& ( ( ap @ X1 @ X5 @ Z0 @ X19 )
= X18 ) ) ) ) )
=> ( in @ X6 @ ( funcSet @ X1 @ X5 ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
thf(c_0_10,negated_conjecture,
! [X20: $i,X21: $i > $o,X22: $i] :
( ( ~ ( in @ X22 @ ( dsetconstr @ X20 @ X21 ) )
| ( in @ X22 @ X20 ) )
& ( in @ esk3_0
@ ( dsetconstr @ ( funcSet @ esk1_0 @ esk2_0 )
@ ^ [Z0: $i] :
! [X18: $i] :
( ( in @ X18 @ esk2_0 )
=> ? [X19: $i] :
( ( in @ X19 @ esk1_0 )
& ( ( ap @ esk1_0 @ esk2_0 @ Z0 @ X19 )
= X18 ) ) ) ) )
& ~ ( in @ esk3_0 @ ( funcSet @ esk1_0 @ esk2_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_9])])])])]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
( in @ esk3_0
@ ( dsetconstr @ ( funcSet @ esk1_0 @ esk2_0 )
@ ^ [Z0: $i] :
! [X26: $i] :
( ( in @ X26 @ esk2_0 )
=> ? [X27: $i] :
( ( in @ X27 @ esk1_0 )
& ( ( ap @ esk1_0 @ esk2_0 @ Z0 @ X27 )
= X26 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ( in @ esk3_0 @ ( funcSet @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU801^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.14 % Computer : n012.cluster.edu
% 0.07/0.14 % Model : x86_64 x86_64
% 0.07/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.14 % Memory : 8046.5625MB
% 0.07/0.14 % OS : Linux 6.8.0-71-generic
% 0.07/0.14 % CPULimit : 300
% 0.07/0.14 % WCLimit : 300
% 0.07/0.14 % DateTime : Tue Sep 29 14:31:48 UTC 2026
% 0.07/0.14 % CPUTime :
% 0.07/0.14 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 Running higher-order theorem proving
% 0.07/0.18 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.KCB2vVDm0r/E---3.1_183459.p
% 0.07/0.19 % Version: 3.5.1-ho
% 0.07/0.19 % Preprocessing class: HSSSSMSSSLMNSFN.
% 0.07/0.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.19 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.19 % Starting sh5l with 300s (1) cores
% 0.07/0.19 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.19 % Starting lpo1_def_fix with 300s (1) cores
% 0.07/0.19 % sh5l with pid 183473 completed with status 0
% 0.07/0.19 % Result found by sh5l
% 0.07/0.19 % Preprocessing class: HSSSSMSSSLMNSFN.
% 0.07/0.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.19 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.19 % Starting sh5l with 300s (1) cores
% 0.07/0.19 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.19 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.19 % Search class: HHUNF-FFSF32-DSFFMFBN
% 0.07/0.19 % partial match(3): HHUSF-FFSF22-SSFFMFBN
% 0.07/0.19 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.19 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.19 % SubtermCWHack with pid 183476 completed with status 0
% 0.07/0.19 % Result found by SubtermCWHack
% 0.07/0.19 % Preprocessing class: HSSSSMSSSLMNSFN.
% 0.07/0.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.19 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.19 % Starting sh5l with 300s (1) cores
% 0.07/0.19 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.19 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.19 % Search class: HHUNF-FFSF32-DSFFMFBN
% 0.07/0.19 % partial match(3): HHUSF-FFSF22-SSFFMFBN
% 0.07/0.19 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.19 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.19 % Preprocessing time : 0.001 s
% 0.07/0.19
% 0.07/0.19 % Proof found!
% 0.07/0.19 % SZS status Theorem
% 0.07/0.19 % SZS output start CNFRefutation
% See solution above
% 0.07/0.19 % Parsed axioms : 11
% 0.07/0.19 % Removed by relevancy pruning/SinE : 7
% 0.07/0.19 % Initial clauses : 3
% 0.07/0.19 % Removed in clause preprocessing : 0
% 0.07/0.19 % Initial clauses in saturation : 3
% 0.07/0.19 % Processed clauses : 3
% 0.07/0.19 % ...of these trivial : 0
% 0.07/0.19 % ...subsumed : 0
% 0.07/0.19 % ...remaining for further processing : 3
% 0.07/0.19 % Other redundant clauses eliminated : 0
% 0.07/0.19 % Clauses deleted for lack of memory : 0
% 0.07/0.19 % Backward-subsumed : 0
% 0.07/0.19 % Backward-rewritten : 0
% 0.07/0.19 % Generated clauses : 1
% 0.07/0.19 % ...of the previous two non-redundant : 0
% 0.07/0.19 % ...aggressively subsumed : 0
% 0.07/0.19 % Contextual simplify-reflections : 0
% 0.07/0.19 % Paramodulations : 1
% 0.07/0.19 % Factorizations : 0
% 0.07/0.19 % NegExts : 0
% 0.07/0.19 % Equation resolutions : 0
% 0.07/0.19 % Disequality decompositions : 0
% 0.07/0.19 % Total rewrite steps : 0
% 0.07/0.19 % ...of those cached : 0
% 0.07/0.19 % Propositional unsat checks : 0
% 0.07/0.19 % Propositional check models : 0
% 0.07/0.19 % Propositional check unsatisfiable : 0
% 0.07/0.19 % Propositional clauses : 0
% 0.07/0.19 % Propositional clauses after purity: 0
% 0.07/0.19 % Propositional unsat core size : 0
% 0.07/0.19 % Propositional preprocessing time : 0.000
% 0.07/0.19 % Propositional encoding time : 0.000
% 0.07/0.19 % Propositional solver time : 0.000
% 0.07/0.19 % Success case prop preproc time : 0.000
% 0.07/0.19 % Success case prop encoding time : 0.000
% 0.07/0.19 % Success case prop solver time : 0.000
% 0.07/0.19 % Current number of processed clauses : 3
% 0.07/0.19 % Positive orientable unit clauses : 1
% 0.07/0.19 % Positive unorientable unit clauses: 0
% 0.07/0.19 % Negative unit clauses : 1
% 0.07/0.19 % Non-unit-clauses : 1
% 0.07/0.19 % Current number of unprocessed clauses: 0
% 0.07/0.19 % ...number of literals in the above : 0
% 0.07/0.19 % Current number of archived formulas : 0
% 0.07/0.19 % Current number of archived clauses : 0
% 0.07/0.19 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.19 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.19 % Non-unit clause-clause subsumptions : 0
% 0.07/0.19 % Unit Clause-clause subsumption calls : 0
% 0.07/0.19 % Rewrite failures with RHS unbound : 0
% 0.07/0.19 % BW rewrite match attempts : 0
% 0.07/0.19 % BW rewrite match successes : 0
% 0.07/0.19 % Condensation attempts : 0
% 0.07/0.19 % Condensation successes : 0
% 0.07/0.19 % Termbank termtop insertions : 628
% 0.07/0.19 % Search garbage collected termcells : 205
% 0.07/0.19
% 0.07/0.19 % -------------------------------------------------
% 0.07/0.19 % User time : 0.003 s
% 0.07/0.19 % System time : 0.001 s
% 0.07/0.19 % Total time : 0.004 s
% 0.07/0.19 % Maximum resident set size: 3852 pages
% 0.07/0.19
% 0.07/0.19 % -------------------------------------------------
% 0.07/0.19 % User time : 0.003 s
% 0.07/0.19 % System time : 0.004 s
% 0.07/0.19 % Total time : 0.008 s
% 0.07/0.19 % Maximum resident set size: 4608 pages
% 0.07/0.19 % E exiting
%------------------------------------------------------------------------------