%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU997^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:26:03 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 82 equ; 0 cnn)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 349 ( 3 ~; 0 |; 56 &; 286 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 6 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 110 ( 0 ^; 108 !; 2 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
esk1_0: a > a > a ).
thf(decl_24,type,
esk2_0: a > a > a ).
thf(decl_25,type,
esk3_0: a ).
thf(decl_26,type,
esk4_0: a ).
thf(decl_27,type,
esk5_1: a > a ).
thf(decl_28,type,
esk6_0: a ).
thf(decl_29,type,
esk7_0: a ).
thf(decl_30,type,
esk8_0: a ).
thf(cCD_LATTICE_THM_pme,conjecture,
! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
( ( ! [X5: a] :
( ( X1 @ X5 @ X5 )
= X5 )
& ! [X5: a] :
( ( X2 @ X5 @ X5 )
= X5 )
& ! [X5: a,X6: a,X7: a] :
( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) )
& ! [X5: a,X6: a,X7: a] :
( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) )
& ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
= ( X1 @ X6 @ X5 ) )
& ! [X5: a,X6: a] :
( ( X2 @ X5 @ X6 )
= ( X2 @ X6 @ X5 ) )
& ! [X5: a,X6: a] :
( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
= X6 )
& ! [X5: a,X6: a] :
( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
= X6 )
& ! [X5: a,X6: a,X7: a] :
( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
= ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) )
& ! [X5: a,X6: a,X7: a] :
( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
= ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) )
& ! [X5: a] :
( ( X2 @ X3 @ X5 )
= X5 )
& ! [X5: a] :
( ( X1 @ X3 @ X5 )
= X3 )
& ! [X5: a] :
( ( X2 @ X4 @ X5 )
= X4 )
& ! [X5: a] :
( ( X1 @ X4 @ X5 )
= X5 )
& ! [X5: a] :
? [X6: a] :
( ( ( X1 @ X5 @ X6 )
= X3 )
& ( ( X2 @ X5 @ X6 )
= X4 ) ) )
=> ! [X5: a,X6: a,X7: a] :
( ( ( ( X1 @ X5 @ X6 )
= X3 )
& ( ( X2 @ X5 @ X6 )
= X4 )
& ( ( X1 @ X5 @ X7 )
= X3 )
& ( ( X2 @ X5 @ X7 )
= X4 ) )
=> ( X6 = X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6tFvVdKIDi/E---3.1_216497.p',cCD_LATTICE_THM_pme) ).
thf(c_0_1,negated_conjecture,
~ ! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
( ( ! [X5: a] :
( ( X1 @ X5 @ X5 )
= X5 )
& ! [X5: a] :
( ( X2 @ X5 @ X5 )
= X5 )
& ! [X5: a,X6: a,X7: a] :
( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
= ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) )
& ! [X5: a,X6: a,X7: a] :
( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
= ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) )
& ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
= ( X1 @ X6 @ X5 ) )
& ! [X5: a,X6: a] :
( ( X2 @ X5 @ X6 )
= ( X2 @ X6 @ X5 ) )
& ! [X5: a,X6: a] :
( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
= X6 )
& ! [X5: a,X6: a] :
( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
= X6 )
& ! [X5: a,X6: a,X7: a] :
( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
= ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) )
& ! [X5: a,X6: a,X7: a] :
( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
= ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) )
& ! [X5: a] :
( ( X2 @ X3 @ X5 )
= X5 )
& ! [X5: a] :
( ( X1 @ X3 @ X5 )
= X3 )
& ! [X5: a] :
( ( X2 @ X4 @ X5 )
= X4 )
& ! [X5: a] :
( ( X1 @ X4 @ X5 )
= X5 )
& ! [X5: a] :
? [X6: a] :
( ( ( X1 @ X5 @ X6 )
= X3 )
& ( ( X2 @ X5 @ X6 )
= X4 ) ) )
=> ! [X5: a,X6: a,X7: a] :
( ( ( ( X1 @ X5 @ X6 )
= X3 )
& ( ( X2 @ X5 @ X6 )
= X4 )
& ( ( X1 @ X5 @ X7 )
= X3 )
& ( ( X2 @ X5 @ X7 )
= X4 ) )
=> ( X6 = X7 ) ) ),
inference(assume_negation,[status(cth)],[cCD_LATTICE_THM_pme]) ).
thf(c_0_2,negated_conjecture,
! [X47: a,X48: a,X49: a,X50: a,X51: a,X52: a,X53: a,X54: a,X55: a,X56: a,X57: a,X58: a,X59: a,X60: a,X61: a,X62: a,X63: a,X64: a,X65: a,X66: a,X67: a,X68: a,X69: a,X70: a,X71: a,X72: a,X73: a] :
( ( ( esk1_0 @ X47 @ X47 )
= X47 )
& ( ( esk2_0 @ X48 @ X48 )
= X48 )
& ( ( esk1_0 @ ( esk1_0 @ X49 @ X50 ) @ X51 )
= ( esk1_0 @ X49 @ ( esk1_0 @ X50 @ X51 ) ) )
& ( ( esk2_0 @ ( esk2_0 @ X52 @ X53 ) @ X54 )
= ( esk2_0 @ X52 @ ( esk2_0 @ X53 @ X54 ) ) )
& ( ( esk1_0 @ X55 @ X56 )
= ( esk1_0 @ X56 @ X55 ) )
& ( ( esk2_0 @ X57 @ X58 )
= ( esk2_0 @ X58 @ X57 ) )
& ( ( esk1_0 @ ( esk2_0 @ X59 @ X60 ) @ X60 )
= X60 )
& ( ( esk2_0 @ ( esk1_0 @ X61 @ X62 ) @ X62 )
= X62 )
& ( ( esk2_0 @ X63 @ ( esk1_0 @ X64 @ X65 ) )
= ( esk1_0 @ ( esk2_0 @ X63 @ X64 ) @ ( esk2_0 @ X63 @ X65 ) ) )
& ( ( esk1_0 @ X66 @ ( esk2_0 @ X67 @ X68 ) )
= ( esk2_0 @ ( esk1_0 @ X66 @ X67 ) @ ( esk1_0 @ X66 @ X68 ) ) )
& ( ( esk2_0 @ esk3_0 @ X69 )
= X69 )
& ( ( esk1_0 @ esk3_0 @ X70 )
= esk3_0 )
& ( ( esk2_0 @ esk4_0 @ X71 )
= esk4_0 )
& ( ( esk1_0 @ esk4_0 @ X72 )
= X72 )
& ( ( esk1_0 @ X73 @ ( esk5_1 @ X73 ) )
= esk3_0 )
& ( ( esk2_0 @ X73 @ ( esk5_1 @ X73 ) )
= esk4_0 )
& ( ( esk1_0 @ esk6_0 @ esk7_0 )
= esk3_0 )
& ( ( esk2_0 @ esk6_0 @ esk7_0 )
= esk4_0 )
& ( ( esk1_0 @ esk6_0 @ esk8_0 )
= esk3_0 )
& ( ( esk2_0 @ esk6_0 @ esk8_0 )
= esk4_0 )
& ( esk7_0 != esk8_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_1])])])])]) ).
thf(c_0_3,negated_conjecture,
( ( esk2_0 @ esk6_0 @ esk8_0 )
= esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X4: a,X3: a] :
( ( esk2_0 @ X3 @ X4 )
= ( esk2_0 @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X3: a] :
( ( esk1_0 @ esk4_0 @ X3 )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
! [X4: a,X3: a] :
( ( esk1_0 @ X3 @ X4 )
= ( esk1_0 @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_7,negated_conjecture,
( ( esk2_0 @ esk6_0 @ esk7_0 )
= esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
! [X3: a,X4: a,X5: a] :
( ( esk2_0 @ X3 @ ( esk1_0 @ X4 @ X5 ) )
= ( esk1_0 @ ( esk2_0 @ X3 @ X4 ) @ ( esk2_0 @ X3 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_9,negated_conjecture,
( ( esk2_0 @ esk8_0 @ esk6_0 )
= esk4_0 ),
inference(rw,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_10,negated_conjecture,
! [X3: a] :
( ( esk1_0 @ X3 @ esk4_0 )
= X3 ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_11,negated_conjecture,
( ( esk1_0 @ esk6_0 @ esk7_0 )
= esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_12,negated_conjecture,
! [X3: a] :
( ( esk2_0 @ esk3_0 @ X3 )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_13,negated_conjecture,
( ( esk2_0 @ esk7_0 @ esk6_0 )
= esk4_0 ),
inference(rw,[status(thm)],[c_0_7,c_0_4]) ).
thf(c_0_14,negated_conjecture,
( ( esk1_0 @ esk6_0 @ esk8_0 )
= esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_15,negated_conjecture,
! [X3: a] :
( ( esk2_0 @ esk8_0 @ ( esk1_0 @ X3 @ esk6_0 ) )
= ( esk2_0 @ esk8_0 @ X3 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_16,negated_conjecture,
( ( esk1_0 @ esk7_0 @ esk6_0 )
= esk3_0 ),
inference(rw,[status(thm)],[c_0_11,c_0_6]) ).
thf(c_0_17,negated_conjecture,
! [X3: a] :
( ( esk2_0 @ X3 @ esk3_0 )
= X3 ),
inference(spm,[status(thm)],[c_0_12,c_0_4]) ).
thf(c_0_18,negated_conjecture,
! [X3: a] :
( ( esk2_0 @ esk7_0 @ ( esk1_0 @ X3 @ esk6_0 ) )
= ( esk2_0 @ esk7_0 @ X3 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_13]),c_0_10]) ).
thf(c_0_19,negated_conjecture,
( ( esk1_0 @ esk8_0 @ esk6_0 )
= esk3_0 ),
inference(rw,[status(thm)],[c_0_14,c_0_6]) ).
thf(c_0_20,negated_conjecture,
( ( esk2_0 @ esk7_0 @ esk8_0 )
= esk8_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_4]) ).
thf(c_0_21,negated_conjecture,
esk7_0 != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17]),c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU997^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E /export/starexec/sandbox2/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 14:57:03 UTC 2026
% 0.07/0.15 % CPUTime :
% 0.07/0.15 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 Running higher-order theorem proving
% 0.07/0.19 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.6tFvVdKIDi/E---3.1_216497.p
% 0.07/0.22 % Version: 3.5.1-ho
% 0.07/0.22 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.07/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.22 % Starting post_as_ho1 with 1500s (5) cores
% 0.07/0.22 % Starting post_as_ho12 with 300s (1) cores
% 0.07/0.22 % Starting new_ho_3 with 300s (1) cores
% 0.07/0.22 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.07/0.22 % post_as_ho1 with pid 216510 completed with status 0
% 0.07/0.22 % Result found by post_as_ho1
% 0.07/0.22 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.07/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.22 % Starting post_as_ho1 with 1500s (5) cores
% 0.07/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.22 % No SInE strategy applied
% 0.07/0.22 % Search class: HUUPM-FFSS11-SSSFFFNN
% 0.07/0.22 % partial match(3): HUUPF-FFSF11-SSSFFMNN
% 0.07/0.22 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.22 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.22 % Starting post_as_ho1 with 151s (1) cores
% 0.07/0.22 % Starting new_ho_8 with 136s (1) cores
% 0.07/0.22 % Starting new_ho_4 with 136s (1) cores
% 0.07/0.22 % Starting post_as_ho5 with 136s (1) cores
% 0.07/0.22 % post_as_ho5 with pid 216518 completed with status 0
% 0.07/0.22 % Result found by post_as_ho5
% 0.07/0.22 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.07/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.22 % Starting post_as_ho1 with 1500s (5) cores
% 0.07/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.22 % No SInE strategy applied
% 0.07/0.22 % Search class: HUUPM-FFSS11-SSSFFFNN
% 0.07/0.22 % partial match(3): HUUPF-FFSF11-SSSFFMNN
% 0.07/0.22 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.22 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.22 % Starting post_as_ho1 with 151s (1) cores
% 0.07/0.22 % Starting new_ho_8 with 136s (1) cores
% 0.07/0.22 % Starting new_ho_4 with 136s (1) cores
% 0.07/0.22 % Starting post_as_ho5 with 136s (1) cores
% 0.07/0.22 % Preprocessing time : 0.001 s
% 0.07/0.22 % Presaturation interreduction done
% 0.07/0.22
% 0.07/0.22 % Proof found!
% 0.07/0.22 % SZS status Theorem
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22 % Parsed axioms : 2
% 0.07/0.22 % Removed by relevancy pruning/SinE : 0
% 0.07/0.22 % Initial clauses : 22
% 0.07/0.22 % Removed in clause preprocessing : 1
% 0.07/0.22 % Initial clauses in saturation : 21
% 0.07/0.22 % Processed clauses : 127
% 0.07/0.22 % ...of these trivial : 27
% 0.07/0.22 % ...subsumed : 9
% 0.07/0.22 % ...remaining for further processing : 91
% 0.07/0.22 % Other redundant clauses eliminated : 0
% 0.07/0.22 % Clauses deleted for lack of memory : 0
% 0.07/0.22 % Backward-subsumed : 0
% 0.07/0.22 % Backward-rewritten : 10
% 0.07/0.22 % Generated clauses : 946
% 0.07/0.22 % ...of the previous two non-redundant : 489
% 0.07/0.22 % ...aggressively subsumed : 0
% 0.07/0.22 % Contextual simplify-reflections : 0
% 0.07/0.22 % Paramodulations : 946
% 0.07/0.22 % Factorizations : 0
% 0.07/0.22 % NegExts : 0
% 0.07/0.22 % Equation resolutions : 0
% 0.07/0.22 % Disequality decompositions : 0
% 0.07/0.22 % Total rewrite steps : 1000
% 0.07/0.22 % ...of those cached : 676
% 0.07/0.22 % Propositional unsat checks : 0
% 0.07/0.22 % Propositional check models : 0
% 0.07/0.22 % Propositional check unsatisfiable : 0
% 0.07/0.22 % Propositional clauses : 0
% 0.07/0.22 % Propositional clauses after purity: 0
% 0.07/0.22 % Propositional unsat core size : 0
% 0.07/0.22 % Propositional preprocessing time : 0.000
% 0.07/0.22 % Propositional encoding time : 0.000
% 0.07/0.22 % Propositional solver time : 0.000
% 0.07/0.22 % Success case prop preproc time : 0.000
% 0.07/0.22 % Success case prop encoding time : 0.000
% 0.07/0.22 % Success case prop solver time : 0.000
% 0.07/0.22 % Current number of processed clauses : 60
% 0.07/0.22 % Positive orientable unit clauses : 55
% 0.07/0.22 % Positive unorientable unit clauses: 4
% 0.07/0.22 % Negative unit clauses : 1
% 0.07/0.22 % Non-unit-clauses : 0
% 0.07/0.22 % Current number of unprocessed clauses: 400
% 0.07/0.22 % ...number of literals in the above : 400
% 0.07/0.22 % Current number of archived formulas : 0
% 0.07/0.22 % Current number of archived clauses : 31
% 0.07/0.22 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.22 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.22 % Non-unit clause-clause subsumptions : 0
% 0.07/0.22 % Unit Clause-clause subsumption calls : 4
% 0.07/0.22 % Rewrite failures with RHS unbound : 0
% 0.07/0.22 % BW rewrite match attempts : 122
% 0.07/0.22 % BW rewrite match successes : 92
% 0.07/0.22 % Condensation attempts : 0
% 0.07/0.22 % Condensation successes : 0
% 0.07/0.22 % Termbank termtop insertions : 14304
% 0.07/0.22 % Search garbage collected termcells : 663
% 0.07/0.22
% 0.07/0.22 % -------------------------------------------------
% 0.07/0.22 % User time : 0.014 s
% 0.07/0.22 % System time : 0.004 s
% 0.07/0.22 % Total time : 0.018 s
% 0.07/0.22 % Maximum resident set size: 3640 pages
% 0.07/0.22
% 0.07/0.22 % -------------------------------------------------
% 0.07/0.22 % User time : 0.084 s
% 0.07/0.22 % System time : 0.014 s
% 0.07/0.22 % Total time : 0.098 s
% 0.07/0.22 % Maximum resident set size: 4864 pages
% 0.07/0.22 % E exiting
%------------------------------------------------------------------------------