%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:36:35 AM UTC 2026
% Result : Theorem 0.10s 0.28s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 4 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 168 ( 16 ~; 10 |; 23 &; 117 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 20 ^; 16 !; 8 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
eps: ( $i > $o ) > $i ).
thf(decl_24,type,
epsio: ( ( $i > $o ) > $o ) > $i > $o ).
thf(decl_25,type,
setunion: ( ( $i > $o ) > $o ) > $i > $o ).
thf(decl_26,type,
choosenonempty: ( ( $i > $o ) > $o ) > $i > $o ).
thf(decl_27,type,
c: ( $i > $o ) > $o ).
thf(decl_28,type,
a: $i ).
thf(decl_29,type,
epred1_0: $i > $o ).
thf(conj,conjecture,
( ( c @ ( choosenonempty @ c ) )
& ? [X2: $i] : ( choosenonempty @ c @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.WEfLqtexNr/E---3.1_949019.p',conj) ).
thf(choosenonemptyd,axiom,
( choosenonempty
= ( ^ [X5: ( $i > $o ) > $o] :
( epsio
@ ^ [X6: $i > $o] :
( ( X5 @ X6 )
& ( X6 @ ( eps @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WEfLqtexNr/E---3.1_949019.p',choosenonemptyd) ).
thf(setuniond,axiom,
( setunion
= ( ^ [X5: ( $i > $o ) > $o,X2: $i] :
? [X6: $i > $o] :
( ( X5 @ X6 )
& ( X6 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WEfLqtexNr/E---3.1_949019.p',setuniond) ).
thf(choiceaxio,axiom,
! [X3: ( $i > $o ) > $o] :
( ? [X4: $i > $o] : ( X3 @ X4 )
=> ( X3 @ ( epsio @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WEfLqtexNr/E---3.1_949019.p',choiceaxio) ).
thf(ca,axiom,
setunion @ c @ a,
file('/export/starexec/sandbox2/tmp/tmp.WEfLqtexNr/E---3.1_949019.p',ca) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WEfLqtexNr/E---3.1_949019.p',choiceax) ).
thf(c_0_6,negated_conjecture,
~ ( ( c @ ( choosenonempty @ c ) )
& ? [X2: $i] : ( choosenonempty @ c @ X2 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_7,plain,
( choosenonempty
= ( ^ [Z0: ( $i > $o ) > $o] :
( epsio
@ ^ [Z1: $i > $o] :
( ( Z0 @ Z1 )
& ( Z1 @ ( eps @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[choosenonemptyd]) ).
thf(c_0_8,negated_conjecture,
~ ( ( c
@ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) ) ) )
& ? [X2: $i] :
( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) )
@ X2 ) ),
inference(apply_def,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,plain,
( setunion
= ( ^ [Z0: ( $i > $o ) > $o,Z1: $i] :
? [X6: $i > $o] :
( ( Z0 @ X6 )
& ( X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[setuniond]) ).
thf(c_0_10,negated_conjecture,
! [X18: $i] :
( ~ ( c
@ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) ) ) )
| ~ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) )
@ X18 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
thf(c_0_11,plain,
! [X15: ( $i > $o ) > $o,X16: $i > $o] :
( ~ ( X15 @ X16 )
| ( X15 @ ( epsio @ X15 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceaxio])])])]) ).
thf(c_0_12,plain,
? [X12: $i > $o] :
( ( c @ X12 )
& ( X12 @ a ) ),
inference(apply_def,[status(thm)],[ca,c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X2: $i] :
( ~ ( c
@ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) ) ) )
| ~ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) )
@ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X3: ( $i > $o ) > $o,X1: $i > $o] :
( ( X3 @ ( epsio @ X3 ) )
| ~ ( X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
! [X13: $i > $o,X14: $i] :
( ~ ( X13 @ X14 )
| ( X13 @ ( eps @ X13 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceax])])])]) ).
thf(c_0_16,plain,
( ( c @ epred1_0 )
& ( epred1_0 @ a ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i > $o] :
( ( ( c
@ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) ) ) )
& ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) )
@ ( eps
@ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) ) ) ) ) )
| ~ ( ( c @ X1 )
& ( X1 @ ( eps @ X1 ) ) ) ),
inference(choice_inst,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
! [X1: $i > $o,X2: $i] :
( ( X1 @ ( eps @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,plain,
epred1_0 @ a,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i > $o] :
( ( c
@ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) ) ) )
| ~ ( X1 @ ( eps @ X1 ) )
| ~ ( c @ X1 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_17]) ).
thf(c_0_21,plain,
epred1_0 @ ( eps @ epred1_0 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_22,plain,
c @ epred1_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,negated_conjecture,
( c
@ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i] :
~ ( epsio
@ ^ [Z0: $i > $o] :
( ( c @ Z0 )
& ( Z0 @ ( eps @ Z0 ) ) )
@ X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_23])]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i > $o] :
( ~ ( X1 @ ( eps @ X1 ) )
| ~ ( c @ X1 ) ),
inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_17]),c_0_24]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n019.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 15:47:03 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 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.WEfLqtexNr/E---3.1_949019.p
% 0.10/0.28 % Version: 3.5.1-ho
% 0.10/0.28 % partial match(1): HSSSSMSSSLSNHHA
% 0.10/0.28 % Preprocessing class: HSSSSMSSSLSCHHA.
% 0.10/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.10/0.28 % Starting sh3l with 300s (1) cores
% 0.10/0.28 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.10/0.28 % Starting full_lambda_8 with 300s (1) cores
% 0.10/0.28 % full_lambda_8 with pid 949055 completed with status 0
% 0.10/0.28 % Result found by full_lambda_8
% 0.10/0.28 % partial match(1): HSSSSMSSSLSNHHA
% 0.10/0.28 % Preprocessing class: HSSSSMSSSLSCHHA.
% 0.10/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.10/0.28 % Starting sh3l with 300s (1) cores
% 0.10/0.28 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.10/0.28 % Starting full_lambda_8 with 300s (1) cores
% 0.10/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.28 % No SInE strategy applied
% 0.10/0.28 % Search class: HHHNF-FFSF11-MHHFMSBC
% 0.10/0.28 % partial match(4): HHUNF-FFSF11-SHHFFSBN
% 0.10/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.28 % SubtermCWHack with pid 949061 completed with status 0
% 0.10/0.28 % Result found by SubtermCWHack
% 0.10/0.28 % partial match(1): HSSSSMSSSLSNHHA
% 0.10/0.28 % Preprocessing class: HSSSSMSSSLSCHHA.
% 0.10/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.10/0.28 % Starting sh3l with 300s (1) cores
% 0.10/0.28 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.10/0.28 % Starting full_lambda_8 with 300s (1) cores
% 0.10/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.28 % No SInE strategy applied
% 0.10/0.28 % Search class: HHHNF-FFSF11-MHHFMSBC
% 0.10/0.28 % partial match(4): HHUNF-FFSF11-SHHFFSBN
% 0.10/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.28 % Preprocessing time : 0.001 s
% 0.10/0.28
% 0.10/0.28 % Proof found!
% 0.10/0.28 % SZS status Theorem
% 0.10/0.28 % SZS output start CNFRefutation
% See solution above
% 0.10/0.28 % Parsed axioms : 12
% 0.10/0.28 % Removed by relevancy pruning/SinE : 0
% 0.10/0.28 % Initial clauses : 11
% 0.10/0.28 % Removed in clause preprocessing : 6
% 0.10/0.28 % Initial clauses in saturation : 5
% 0.10/0.28 % Processed clauses : 13
% 0.10/0.28 % ...of these trivial : 0
% 0.10/0.28 % ...subsumed : 0
% 0.10/0.28 % ...remaining for further processing : 13
% 0.10/0.28 % Other redundant clauses eliminated : 0
% 0.10/0.28 % Clauses deleted for lack of memory : 0
% 0.10/0.28 % Backward-subsumed : 0
% 0.10/0.28 % Backward-rewritten : 2
% 0.10/0.28 % Generated clauses : 13
% 0.10/0.28 % ...of the previous two non-redundant : 10
% 0.10/0.28 % ...aggressively subsumed : 0
% 0.10/0.28 % Contextual simplify-reflections : 0
% 0.10/0.28 % Paramodulations : 7
% 0.10/0.28 % Factorizations : 0
% 0.10/0.28 % NegExts : 0
% 0.10/0.28 % Equation resolutions : 0
% 0.10/0.28 % Disequality decompositions : 0
% 0.10/0.28 % Total rewrite steps : 7
% 0.10/0.28 % ...of those cached : 3
% 0.10/0.28 % Propositional unsat checks : 0
% 0.10/0.28 % Propositional check models : 0
% 0.10/0.28 % Propositional check unsatisfiable : 0
% 0.10/0.28 % Propositional clauses : 0
% 0.10/0.28 % Propositional clauses after purity: 0
% 0.10/0.28 % Propositional unsat core size : 0
% 0.10/0.28 % Propositional preprocessing time : 0.000
% 0.10/0.28 % Propositional encoding time : 0.000
% 0.10/0.28 % Propositional solver time : 0.000
% 0.10/0.28 % Success case prop preproc time : 0.000
% 0.10/0.28 % Success case prop encoding time : 0.000
% 0.10/0.28 % Success case prop solver time : 0.000
% 0.10/0.28 % Current number of processed clauses : 9
% 0.10/0.28 % Positive orientable unit clauses : 5
% 0.10/0.28 % Positive unorientable unit clauses: 0
% 0.10/0.28 % Negative unit clauses : 1
% 0.10/0.28 % Non-unit-clauses : 3
% 0.10/0.28 % Current number of unprocessed clauses: 2
% 0.10/0.28 % ...number of literals in the above : 6
% 0.10/0.28 % Current number of archived formulas : 0
% 0.10/0.28 % Current number of archived clauses : 4
% 0.10/0.28 % Clause-clause subsumption calls (NU) : 15
% 0.10/0.28 % Rec. Clause-clause subsumption calls : 15
% 0.10/0.28 % Non-unit clause-clause subsumptions : 0
% 0.10/0.28 % Unit Clause-clause subsumption calls : 0
% 0.10/0.28 % Rewrite failures with RHS unbound : 0
% 0.10/0.28 % BW rewrite match attempts : 1
% 0.10/0.28 % BW rewrite match successes : 1
% 0.10/0.28 % Condensation attempts : 0
% 0.10/0.28 % Condensation successes : 0
% 0.10/0.28 % Termbank termtop insertions : 2847
% 0.10/0.28 % Search garbage collected termcells : 110
% 0.10/0.28
% 0.10/0.28 % -------------------------------------------------
% 0.10/0.28 % User time : 0.003 s
% 0.10/0.28 % System time : 0.005 s
% 0.10/0.28 % Total time : 0.008 s
% 0.10/0.28 % Maximum resident set size: 3640 pages
% 0.10/0.28
% 0.10/0.28 % -------------------------------------------------
% 0.10/0.28 % User time : 0.005 s
% 0.10/0.28 % System time : 0.009 s
% 0.10/0.28 % Total time : 0.014 s
% 0.10/0.28 % Maximum resident set size: 4864 pages
% 0.10/0.28 % E exiting
%------------------------------------------------------------------------------