%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO379^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:44:18 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 23 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 51 ( 10 ~; 9 |; 5 &; 26 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 10 ^; 8 !; 7 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
c: $i ).
thf(decl_24,type,
cQDP0: $i > $o ).
thf(decl_25,type,
cQDP1: ( $i > $o ) > $o ).
thf(decl_26,type,
esk1_1: ( $i > $o ) > $i ).
thf(cQDP1_def,axiom,
( cQDP1
= ( ^ [X2: $i > $o] :
( ( X2 = cQDP0 )
& ? [X3: $i] : ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qnX15RtfOW/E---3.1_337058.p',cQDP1_def) ).
thf(cQDP0_def,axiom,
( cQDP0
= ( ^ [X1: $i] : ( X1 = c ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qnX15RtfOW/E---3.1_337058.p',cQDP0_def) ).
thf(cQDTHM1,conjecture,
? [X4: $i > $o] : ( cQDP1 @ X4 ),
file('/export/starexec/sandbox/tmp/tmp.qnX15RtfOW/E---3.1_337058.p',cQDTHM1) ).
thf(c_0_3,plain,
( cQDP1
= ( ^ [Z0: $i > $o] :
( ( Z0
= ( ^ [Z1: $i] : ( Z1 = c ) ) )
& ? [X3: $i] : ( Z0 @ X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[cQDP1_def]) ).
thf(c_0_4,plain,
( cQDP0
= ( ^ [Z0: $i] : ( Z0 = c ) ) ),
inference(fof_simplification,[status(thm)],[cQDP0_def]) ).
thf(c_0_5,negated_conjecture,
~ ? [X4: $i > $o] : ( cQDP1 @ X4 ),
inference(assume_negation,[status(cth)],[cQDTHM1]) ).
thf(c_0_6,plain,
( cQDP1
= ( ^ [Z0: $i > $o] :
( ( Z0
= ( ^ [Z1: $i] : ( Z1 = c ) ) )
& ? [X3: $i] : ( Z0 @ X3 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_7,negated_conjecture,
~ ? [X4: $i > $o] :
( ! [X7: $i] :
( ( X4 @ X7 )
<=> ( X7 = c ) )
& ? [X6: $i] : ( X4 @ X6 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6])]) ).
thf(c_0_8,negated_conjecture,
! [X8: $i > $o,X10: $i] :
( ( ~ ( X8 @ ( esk1_1 @ X8 ) )
| ( ( esk1_1 @ X8 )
!= c )
| ~ ( X8 @ X10 ) )
& ( ( X8 @ ( esk1_1 @ X8 ) )
| ( ( esk1_1 @ X8 )
= c )
| ~ ( X8 @ X10 ) ) ),
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_7])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( X2 @ ( esk1_1 @ X2 ) )
| ( ( esk1_1 @ X2 )
= c )
| ~ ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i] :
( ( ( esk1_1
@ ^ [Z0: $i] : ( Z0 = X1 ) )
= c )
| ( ( esk1_1
@ ^ [Z0: $i] : ( Z0 = X1 ) )
= X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ~ ( X2 @ ( esk1_1 @ X2 ) )
| ( ( esk1_1 @ X2 )
!= c )
| ~ ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
( ( esk1_1
@ ^ [Z0: $i] : ( Z0 = c ) )
= c ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_10])]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12])])])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO379^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n011.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 16:50:01 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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.qnX15RtfOW/E---3.1_337058.p
% 0.09/0.24 % Version: 3.5.1-ho
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLSNHSN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.24 % Starting lpo8_lambda_fix with 300s (1) cores
% 0.09/0.24 % Starting lpo8_s with 300s (1) cores
% 0.09/0.24 % Starting new_bool_11 with 300s (1) cores
% 0.09/0.24 % ho_unfolding_3 with pid 337071 completed with status 0
% 0.09/0.24 % Result found by ho_unfolding_3
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLSNHSN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HGHSF-FFSF11-SHSFMMBN
% 0.09/0.24 % partial match(1): HGHSF-FFSF21-SHSFMMBN
% 0.09/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.24 % Starting ho_unfolding_3 with 151s (1) cores
% 0.09/0.24 % Starting sh5l with 136s (1) cores
% 0.09/0.24 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.24 % Starting new_bool_2 with 136s (1) cores
% 0.09/0.24 % SubtermCWHack with pid 337075 completed with status 10
% 0.09/0.24 % Starting new_bool_9 with 136s (1) cores
% 0.09/0.24 % ho_unfolding_3 with pid 337078 completed with status 0
% 0.09/0.24 % Result found by ho_unfolding_3
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLSNHSN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HGHSF-FFSF11-SHSFMMBN
% 0.09/0.24 % partial match(1): HGHSF-FFSF21-SHSFMMBN
% 0.09/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.24 % Starting ho_unfolding_3 with 151s (1) cores
% 0.09/0.24 % Preprocessing time : 0.001 s
% 0.09/0.24 % Presaturation interreduction done
% 0.09/0.24
% 0.09/0.24 % Proof found!
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24 % Parsed axioms : 6
% 0.09/0.24 % Removed by relevancy pruning/SinE : 0
% 0.09/0.24 % Initial clauses : 5
% 0.09/0.24 % Removed in clause preprocessing : 3
% 0.09/0.24 % Initial clauses in saturation : 2
% 0.09/0.24 % Processed clauses : 7
% 0.09/0.24 % ...of these trivial : 0
% 0.09/0.24 % ...subsumed : 0
% 0.09/0.24 % ...remaining for further processing : 7
% 0.09/0.24 % Other redundant clauses eliminated : 7
% 0.09/0.24 % Clauses deleted for lack of memory : 0
% 0.09/0.24 % Backward-subsumed : 0
% 0.09/0.24 % Backward-rewritten : 0
% 0.09/0.24 % Generated clauses : 18
% 0.09/0.24 % ...of the previous two non-redundant : 10
% 0.09/0.24 % ...aggressively subsumed : 0
% 0.09/0.24 % Contextual simplify-reflections : 0
% 0.09/0.24 % Paramodulations : 3
% 0.09/0.24 % Factorizations : 2
% 0.09/0.24 % NegExts : 1
% 0.09/0.24 % Equation resolutions : 8
% 0.09/0.24 % Disequality decompositions : 0
% 0.09/0.24 % Total rewrite steps : 0
% 0.09/0.24 % ...of those cached : 0
% 0.09/0.24 % Propositional unsat checks : 0
% 0.09/0.24 % Propositional check models : 0
% 0.09/0.24 % Propositional check unsatisfiable : 0
% 0.09/0.24 % Propositional clauses : 0
% 0.09/0.24 % Propositional clauses after purity: 0
% 0.09/0.24 % Propositional unsat core size : 0
% 0.09/0.24 % Propositional preprocessing time : 0.000
% 0.09/0.24 % Propositional encoding time : 0.000
% 0.09/0.24 % Propositional solver time : 0.000
% 0.09/0.24 % Success case prop preproc time : 0.000
% 0.09/0.24 % Success case prop encoding time : 0.000
% 0.09/0.24 % Success case prop solver time : 0.000
% 0.09/0.24 % Current number of processed clauses : 5
% 0.09/0.24 % Positive orientable unit clauses : 1
% 0.09/0.24 % Positive unorientable unit clauses: 0
% 0.09/0.24 % Negative unit clauses : 0
% 0.09/0.24 % Non-unit-clauses : 4
% 0.09/0.24 % Current number of unprocessed clauses: 7
% 0.09/0.24 % ...number of literals in the above : 18
% 0.09/0.24 % Current number of archived formulas : 0
% 0.09/0.24 % Current number of archived clauses : 2
% 0.09/0.24 % Clause-clause subsumption calls (NU) : 6
% 0.09/0.24 % Rec. Clause-clause subsumption calls : 3
% 0.09/0.24 % Non-unit clause-clause subsumptions : 0
% 0.09/0.24 % Unit Clause-clause subsumption calls : 2
% 0.09/0.24 % Rewrite failures with RHS unbound : 0
% 0.09/0.24 % BW rewrite match attempts : 0
% 0.09/0.24 % BW rewrite match successes : 0
% 0.09/0.24 % Condensation attempts : 7
% 0.09/0.24 % Condensation successes : 0
% 0.09/0.24 % Termbank termtop insertions : 638
% 0.09/0.24 % Search garbage collected termcells : 98
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.004 s
% 0.09/0.24 % System time : 0.004 s
% 0.09/0.24 % Total time : 0.008 s
% 0.09/0.24 % Maximum resident set size: 3628 pages
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.013 s
% 0.09/0.24 % System time : 0.013 s
% 0.09/0.24 % Total time : 0.026 s
% 0.09/0.24 % Maximum resident set size: 4608 pages
% 0.09/0.24 % E exiting
%------------------------------------------------------------------------------