%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU796^2 : 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 08:25:40 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 12 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 155 ( 14 ~; 9 |; 10 &; 111 @)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 47 ( 6 ^; 35 !; 6 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
image1: $i > ( $i > $i ) > $i ).
thf(decl_25,type,
image1Equiv: $o ).
thf(decl_26,type,
esk1_3: $i > ( $i > $i ) > $i > $i ).
thf(decl_27,type,
esk2_0: $i ).
thf(decl_28,type,
esk3_0: $i > $i ).
thf(decl_29,type,
esk4_0: $i ).
thf(image1E,conjecture,
( image1Equiv
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( image1 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( X3
= ( X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ftjYWJB8Hz/E---3.1_804830.p',image1E) ).
thf(image1Equiv,axiom,
( image1Equiv
<=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( image1 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
<=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( X3
= ( X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ftjYWJB8Hz/E---3.1_804830.p',image1Equiv) ).
thf(c_0_2,negated_conjecture,
~ ( image1Equiv
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( image1 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( X3
= ( X2 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[image1E]) ).
thf(c_0_3,plain,
( image1Equiv
<=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( image1 @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
<=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( X3
= ( X2 @ X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[image1Equiv]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X13: $i,X14: $i > $i,X15: $i] :
( ( in @ X15
@ ( image1 @ X13
@ ^ [Z0: $i] : ( X14 @ Z0 ) ) )
<=> ? [X16: $i] :
( ( in @ X16 @ X13 )
& ( X15
= ( X14 @ X16 ) ) ) )
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( image1 @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( X3
= ( X2 @ X4 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2]),c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X17: $i,X18: $i > $i,X19: $i,X21: $i,X22: $i > $i,X23: $i,X24: $i,X28: $i] :
( ( ( in @ ( esk1_3 @ X17 @ X18 @ X19 ) @ X17 )
| ~ ( in @ X19 @ ( image1 @ X17 @ X18 ) ) )
& ( ( X19
= ( X18 @ ( esk1_3 @ X17 @ X18 @ X19 ) ) )
| ~ ( in @ X19 @ ( image1 @ X17 @ X18 ) ) )
& ( ~ ( in @ X24 @ X21 )
| ( X23
!= ( X22 @ X24 ) )
| ( in @ X23 @ ( image1 @ X21 @ X22 ) ) )
& ( in @ esk4_0 @ ( image1 @ esk2_0 @ esk3_0 ) )
& ( ~ ( in @ X28 @ esk2_0 )
| ( esk4_0
!= ( esk3_0 @ X28 ) ) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk2_0 )
| ( esk4_0
!= ( esk3_0 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ~ ( in @ X3 @ ( image1 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i > $i] :
( ( ( esk3_0 @ ( esk1_3 @ esk2_0 @ X2 @ X1 ) )
!= esk4_0 )
| ~ ( in @ X1 @ ( image1 @ esk2_0 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $i] :
( ( X1
= ( X2 @ ( esk1_3 @ X3 @ X2 @ X1 ) ) )
| ~ ( in @ X1 @ ( image1 @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
in @ esk4_0 @ ( image1 @ esk2_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9])]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU796^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:31:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.ftjYWJB8Hz/E---3.1_804830.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLMNSSA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_9 with 300s (1) cores
% 0.07/0.25 % new_bool_2 with pid 804845 completed with status 0
% 0.07/0.25 % Result found by new_bool_2
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLMNSSA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.25 % Search class: HHHSF-FFSF32-SSSFMSNN
% 0.07/0.25 % partial match(3): HHUSF-FFSF32-SHSFMSBN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 804850 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLMNSSA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.25 % Search class: HHHSF-FFSF32-SSSFMSNN
% 0.07/0.25 % partial match(3): HHUSF-FFSF32-SHSFMSBN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 5
% 0.07/0.25 % Removed by relevancy pruning/SinE : 3
% 0.07/0.25 % Initial clauses : 5
% 0.07/0.25 % Removed in clause preprocessing : 0
% 0.07/0.25 % Initial clauses in saturation : 5
% 0.07/0.25 % Processed clauses : 7
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 7
% 0.07/0.25 % Other redundant clauses eliminated : 2
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 0
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 8
% 0.07/0.25 % ...of the previous two non-redundant : 6
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 6
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 2
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 1
% 0.07/0.25 % ...of those cached : 0
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 6
% 0.07/0.25 % Positive orientable unit clauses : 1
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 0
% 0.07/0.25 % Non-unit-clauses : 5
% 0.07/0.25 % Current number of unprocessed clauses: 3
% 0.07/0.25 % ...number of literals in the above : 9
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 0
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 3
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 3
% 0.07/0.25 % Non-unit clause-clause subsumptions : 0
% 0.07/0.25 % Unit Clause-clause subsumption calls : 0
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 0
% 0.07/0.25 % BW rewrite match successes : 0
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 665
% 0.07/0.25 % Search garbage collected termcells : 214
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.003 s
% 0.07/0.25 % System time : 0.001 s
% 0.07/0.25 % Total time : 0.004 s
% 0.07/0.25 % Maximum resident set size: 3632 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.003 s
% 0.07/0.25 % System time : 0.006 s
% 0.07/0.25 % Total time : 0.009 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------