%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV181^5 : 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 : n005.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 08:35:09 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 26 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 102 ( 19 ~; 4 |; 11 &; 61 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 9 ^; 16 !; 9 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
thf(decl_24,type,
esk1_0: ( $i > $o ) > $i ).
thf(decl_25,type,
epred1_0: $i > $o ).
thf(cTHM143C_pme,conjecture,
! [X1: ( $i > $o ) > $i] :
( ! [X4: $i > $o,X5: $i > $o] :
( ( ( X1 @ X4 )
= ( X1 @ X5 ) )
=> ( X4 = X5 ) )
=> ~ ( cD_FOR_X5309 @ X1 @ ( X1 @ ( cD_FOR_X5309 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZfgP1D7HFJ/E---3.1_1791805.p',cTHM143C_pme) ).
thf(cD_FOR_X5309_def,axiom,
( cD_FOR_X5309
= ( ^ [X1: ( $i > $o ) > $i,X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X1 @ X3 ) )
& ( X2
= ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZfgP1D7HFJ/E---3.1_1791805.p',cD_FOR_X5309_def) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i] :
( ! [X4: $i > $o,X5: $i > $o] :
( ( ( X1 @ X4 )
= ( X1 @ X5 ) )
=> ( X4 = X5 ) )
=> ~ ( cD_FOR_X5309 @ X1 @ ( X1 @ ( cD_FOR_X5309 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM143C_pme]) ).
thf(c_0_3,plain,
( cD_FOR_X5309
= ( ^ [Z0: ( $i > $o ) > $i,Z1: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( Z0 @ X3 ) )
& ( Z1
= ( Z0 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cD_FOR_X5309_def]) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i] :
( ! [X4: $i > $o,X5: $i > $o] :
( ( ( X1 @ X4 )
= ( X1 @ X5 ) )
=> ( X4 = X5 ) )
=> ~ ? [X10: $i > $o] :
( ~ ( X10 @ ( X1 @ X10 ) )
& ( ( X1
@ ^ [Z0: $i] :
? [X9: $i > $o] :
( ~ ( X9 @ ( X1 @ X9 ) )
& ( Z0
= ( X1 @ X9 ) ) ) )
= ( X1 @ X10 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_2,c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X12: $i > $o,X13: $i > $o] :
( ( ( ( esk1_0 @ X12 )
!= ( esk1_0 @ X13 ) )
| ( X12 = X13 ) )
& ~ ( epred1_0 @ ( esk1_0 @ epred1_0 ) )
& ( ( esk1_0
@ ^ [Z0: $i] :
? [X9: $i > $o] :
( ~ ( X9 @ ( esk1_0 @ X9 ) )
& ( Z0
= ( esk1_0 @ X9 ) ) ) )
= ( esk1_0 @ epred1_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_4])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X3: $i > $o,X4: $i > $o] :
( ( X3 = X4 )
| ( ( esk1_0 @ X3 )
!= ( esk1_0 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
( ( esk1_0
@ ^ [Z0: $i] :
? [X31: $i > $o] :
( ~ ( X31 @ ( esk1_0 @ X31 ) )
& ( Z0
= ( esk1_0 @ X31 ) ) ) )
= ( esk1_0 @ epred1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i > $o] :
( ( ( ^ [Z0: $i] :
? [X32: $i > $o] :
( ~ ( X32 @ ( esk1_0 @ X32 ) )
& ( Z0
= ( esk1_0 @ X32 ) ) ) )
= X3 )
| ( ( esk1_0 @ epred1_0 )
!= ( esk1_0 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
( ( ^ [Z0: $i] :
? [X33: $i > $o] :
( ~ ( X33 @ ( esk1_0 @ X33 ) )
& ( Z0
= ( esk1_0 @ X33 ) ) ) )
= epred1_0 ),
inference(er,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X20: $i] :
( ? [X34: $i > $o] :
( ~ ( X34 @ ( esk1_0 @ X34 ) )
& ( X20
= ( esk1_0 @ X34 ) ) )
<=> ( epred1_0 @ X20 ) ),
inference(arg_cong,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i > $o] :
( ( epred1_0 @ ( esk1_0 @ X3 ) )
| ( X3 @ ( esk1_0 @ X3 ) ) ),
inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_10])]) ).
thf(c_0_12,negated_conjecture,
~ ( epred1_0 @ ( esk1_0 @ epred1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV181^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n005.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 15:19:01 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running higher-order theorem proving
% 0.24/0.31 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.ZfgP1D7HFJ/E---3.1_1791805.p
% 0.24/0.33 % Version: 3.5.1-ho
% 0.24/0.33 % Preprocessing class: HSSSSMSSSLSNHHA.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.33 % Starting sh3l with 300s (1) cores
% 0.24/0.33 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.24/0.33 % Starting full_lambda_8 with 300s (1) cores
% 0.24/0.33 % full_lambda_8 with pid 1791821 completed with status 0
% 0.24/0.33 % Result found by full_lambda_8
% 0.24/0.33 % Preprocessing class: HSSSSMSSSLSNHHA.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.33 % Starting sh3l with 300s (1) cores
% 0.24/0.33 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.24/0.33 % Starting full_lambda_8 with 300s (1) cores
% 0.24/0.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.33 % No SInE strategy applied
% 0.24/0.33 % Search class: HHUSF-FFSF00-DHHFMFBN
% 0.24/0.33 % partial match(3): HHUPF-FFSF00-SHHFFFBN
% 0.24/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.33 % SubtermCWHack with pid 1791824 completed with status 0
% 0.24/0.33 % Result found by SubtermCWHack
% 0.24/0.33 % Preprocessing class: HSSSSMSSSLSNHHA.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.33 % Starting sh3l with 300s (1) cores
% 0.24/0.33 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.24/0.33 % Starting full_lambda_8 with 300s (1) cores
% 0.24/0.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.33 % No SInE strategy applied
% 0.24/0.33 % Search class: HHUSF-FFSF00-DHHFMFBN
% 0.24/0.33 % partial match(3): HHUPF-FFSF00-SHHFFFBN
% 0.24/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.33 % Preprocessing time : 0.002 s
% 0.24/0.33
% 0.24/0.33 % Proof found!
% 0.24/0.33 % SZS status Theorem
% 0.24/0.33 % SZS output start CNFRefutation
% See solution above
% 0.24/0.33 % Parsed axioms : 3
% 0.24/0.33 % Removed by relevancy pruning/SinE : 0
% 0.24/0.33 % Initial clauses : 4
% 0.24/0.33 % Removed in clause preprocessing : 1
% 0.24/0.33 % Initial clauses in saturation : 3
% 0.24/0.34 % Processed clauses : 12
% 0.24/0.34 % ...of these trivial : 0
% 0.24/0.34 % ...subsumed : 2
% 0.24/0.34 % ...remaining for further processing : 10
% 0.24/0.34 % Other redundant clauses eliminated : 2
% 0.24/0.34 % Clauses deleted for lack of memory : 0
% 0.24/0.34 % Backward-subsumed : 0
% 0.24/0.34 % Backward-rewritten : 2
% 0.24/0.34 % Generated clauses : 22
% 0.24/0.34 % ...of the previous two non-redundant : 17
% 0.24/0.34 % ...aggressively subsumed : 0
% 0.24/0.34 % Contextual simplify-reflections : 0
% 0.24/0.34 % Paramodulations : 4
% 0.24/0.34 % Factorizations : 2
% 0.24/0.34 % NegExts : 0
% 0.24/0.34 % Equation resolutions : 5
% 0.24/0.34 % Disequality decompositions : 0
% 0.24/0.34 % Total rewrite steps : 2
% 0.24/0.34 % ...of those cached : 1
% 0.24/0.34 % Propositional unsat checks : 0
% 0.24/0.34 % Propositional check models : 0
% 0.24/0.34 % Propositional check unsatisfiable : 0
% 0.24/0.34 % Propositional clauses : 0
% 0.24/0.34 % Propositional clauses after purity: 0
% 0.24/0.34 % Propositional unsat core size : 0
% 0.24/0.34 % Propositional preprocessing time : 0.000
% 0.24/0.34 % Propositional encoding time : 0.000
% 0.24/0.34 % Propositional solver time : 0.000
% 0.24/0.34 % Success case prop preproc time : 0.000
% 0.24/0.34 % Success case prop encoding time : 0.000
% 0.24/0.34 % Success case prop solver time : 0.000
% 0.24/0.34 % Current number of processed clauses : 5
% 0.24/0.34 % Positive orientable unit clauses : 1
% 0.24/0.34 % Positive unorientable unit clauses: 0
% 0.24/0.34 % Negative unit clauses : 1
% 0.24/0.34 % Non-unit-clauses : 3
% 0.24/0.34 % Current number of unprocessed clauses: 5
% 0.24/0.34 % ...number of literals in the above : 13
% 0.24/0.34 % Current number of archived formulas : 0
% 0.24/0.34 % Current number of archived clauses : 5
% 0.24/0.34 % Clause-clause subsumption calls (NU) : 8
% 0.24/0.34 % Rec. Clause-clause subsumption calls : 8
% 0.24/0.34 % Non-unit clause-clause subsumptions : 2
% 0.24/0.34 % Unit Clause-clause subsumption calls : 0
% 0.24/0.34 % Rewrite failures with RHS unbound : 0
% 0.24/0.34 % BW rewrite match attempts : 1
% 0.24/0.34 % BW rewrite match successes : 1
% 0.24/0.34 % Condensation attempts : 0
% 0.24/0.34 % Condensation successes : 0
% 0.24/0.34 % Termbank termtop insertions : 1707
% 0.24/0.34 % Search garbage collected termcells : 156
% 0.24/0.34
% 0.24/0.34 % -------------------------------------------------
% 0.24/0.34 % User time : 0.005 s
% 0.24/0.34 % System time : 0.004 s
% 0.24/0.34 % Total time : 0.009 s
% 0.24/0.34 % Maximum resident set size: 3632 pages
% 0.24/0.34
% 0.24/0.34 % -------------------------------------------------
% 0.24/0.34 % User time : 0.007 s
% 0.24/0.34 % System time : 0.008 s
% 0.24/0.34 % Total time : 0.015 s
% 0.24/0.34 % Maximum resident set size: 4864 pages
% 0.24/0.34 % E exiting
%------------------------------------------------------------------------------