%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU996^5 : 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 : n002.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 0.22s 0.36s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 47 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 291 ( 4 ~; 0 |; 29 &; 254 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 0 ^; 88 !; 0 ?; 88 :)
% 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_0: a ).
thf(cMODULAR_THM_pme,conjecture,
! [X1: a > a > a,X2: a > a > a] :
( ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
& ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 )
& ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
& ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) )
& ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) )
& ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) )
& ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 )
& ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 )
& ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) )
& ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZZlbXt89iW/E---3.1_1403417.p',cMODULAR_THM_pme) ).
thf(c_0_1,negated_conjecture,
~ ! [X1: a > a > a,X2: a > a > a] :
( ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
& ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 )
& ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
& ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) )
& ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) )
& ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) )
& ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 )
& ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 )
& ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) )
& ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[cMODULAR_THM_pme]) ).
thf(c_0_2,negated_conjecture,
! [X35: a,X36: a,X37: a,X38: a,X39: a,X40: a,X41: a,X42: a,X43: a,X44: a,X45: a,X46: a,X47: a,X48: a,X49: a,X50: a,X51: a,X52: a,X53: a,X54: a,X55: a,X56: a] :
( ( ( esk1_0 @ X35 @ X35 )
= X35 )
& ( ( esk2_0 @ X36 @ X36 )
= X36 )
& ( ( esk1_0 @ ( esk1_0 @ X37 @ X38 ) @ X39 )
= ( esk1_0 @ X37 @ ( esk1_0 @ X38 @ X39 ) ) )
& ( ( esk2_0 @ ( esk2_0 @ X40 @ X41 ) @ X42 )
= ( esk2_0 @ X40 @ ( esk2_0 @ X41 @ X42 ) ) )
& ( ( esk1_0 @ X43 @ X44 )
= ( esk1_0 @ X44 @ X43 ) )
& ( ( esk2_0 @ X45 @ X46 )
= ( esk2_0 @ X46 @ X45 ) )
& ( ( esk1_0 @ ( esk2_0 @ X47 @ X48 ) @ X48 )
= X48 )
& ( ( esk2_0 @ ( esk1_0 @ X49 @ X50 ) @ X50 )
= X50 )
& ( ( esk1_0 @ X51 @ ( esk2_0 @ X52 @ X53 ) )
= ( esk2_0 @ ( esk1_0 @ X51 @ X52 ) @ ( esk1_0 @ X51 @ X53 ) ) )
& ( ( esk2_0 @ X54 @ ( esk1_0 @ X55 @ X56 ) )
= ( esk1_0 @ ( esk2_0 @ X54 @ X55 ) @ ( esk2_0 @ X54 @ X56 ) ) )
& ( ( esk1_0 @ esk3_0 @ esk5_0 )
= esk5_0 )
& ( ( esk1_0 @ esk3_0 @ ( esk2_0 @ esk4_0 @ esk5_0 ) )
!= ( esk2_0 @ ( esk1_0 @ esk3_0 @ esk4_0 ) @ esk5_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,
! [X3: a,X4: a] :
( ( esk2_0 @ ( esk1_0 @ X3 @ X4 ) @ X4 )
= X4 ),
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,
( ( esk1_0 @ esk3_0 @ esk5_0 )
= esk5_0 ),
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,
! [X4: a,X3: a] :
( ( esk2_0 @ X3 @ ( esk1_0 @ X4 @ X3 ) )
= X3 ),
inference(rw,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_8,negated_conjecture,
( ( esk1_0 @ esk5_0 @ esk3_0 )
= esk5_0 ),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_9,negated_conjecture,
( ( esk1_0 @ esk3_0 @ ( esk2_0 @ esk4_0 @ esk5_0 ) )
!= ( esk2_0 @ ( esk1_0 @ esk3_0 @ esk4_0 ) @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_10,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_11,negated_conjecture,
( ( esk2_0 @ esk5_0 @ esk3_0 )
= esk3_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_4]) ).
thf(c_0_12,negated_conjecture,
( ( esk2_0 @ esk5_0 @ ( esk1_0 @ esk3_0 @ esk4_0 ) )
!= ( esk1_0 @ esk3_0 @ ( esk2_0 @ esk5_0 @ esk4_0 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_4]),c_0_4]) ).
thf(c_0_13,negated_conjecture,
! [X3: a] :
( ( esk2_0 @ esk5_0 @ ( esk1_0 @ esk3_0 @ X3 ) )
= ( esk1_0 @ esk3_0 @ ( esk2_0 @ esk5_0 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU996^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n002.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Tue Sep 29 14:59:52 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.30 Running higher-order theorem proving
% 0.22/0.31 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.ZZlbXt89iW/E---3.1_1403417.p
% 0.22/0.36 % Version: 3.5.1-ho
% 0.22/0.36 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.22/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.36 % Starting post_as_ho1 with 1500s (5) cores
% 0.22/0.36 % Starting post_as_ho12 with 300s (1) cores
% 0.22/0.36 % Starting new_ho_3 with 300s (1) cores
% 0.22/0.36 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.36 % post_as_ho1 with pid 1403430 completed with status 0
% 0.22/0.36 % Result found by post_as_ho1
% 0.22/0.36 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.22/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.36 % Starting post_as_ho1 with 1500s (5) cores
% 0.22/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.36 % No SInE strategy applied
% 0.22/0.36 % Search class: HUUPM-FFSF00-SSSFFFNN
% 0.22/0.36 % partial match(1): HUUPF-FFSF00-SSSFFFNN
% 0.22/0.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.36 % Starting post_as_ho1 with 151s (1) cores
% 0.22/0.36 % Starting sh5l with 136s (1) cores
% 0.22/0.36 % Starting new_bool_1 with 136s (1) cores
% 0.22/0.36 % Starting new_bool_2 with 136s (1) cores
% 0.22/0.36 % post_as_ho1 with pid 1403436 completed with status 0
% 0.22/0.36 % Result found by post_as_ho1
% 0.22/0.36 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.22/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.36 % Starting post_as_ho1 with 1500s (5) cores
% 0.22/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.36 % No SInE strategy applied
% 0.22/0.36 % Search class: HUUPM-FFSF00-SSSFFFNN
% 0.22/0.36 % partial match(1): HUUPF-FFSF00-SSSFFFNN
% 0.22/0.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.36 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.36 % Starting post_as_ho1 with 151s (1) cores
% 0.22/0.36 % Preprocessing time : 0.002 s
% 0.22/0.36 % Presaturation interreduction done
% 0.22/0.36
% 0.22/0.36 % Proof found!
% 0.22/0.36 % SZS status Theorem
% 0.22/0.36 % SZS output start CNFRefutation
% See solution above
% 0.22/0.36 % Parsed axioms : 2
% 0.22/0.36 % Removed by relevancy pruning/SinE : 0
% 0.22/0.36 % Initial clauses : 13
% 0.22/0.36 % Removed in clause preprocessing : 1
% 0.22/0.36 % Initial clauses in saturation : 12
% 0.22/0.36 % Processed clauses : 80
% 0.22/0.36 % ...of these trivial : 17
% 0.22/0.36 % ...subsumed : 12
% 0.22/0.36 % ...remaining for further processing : 51
% 0.22/0.36 % Other redundant clauses eliminated : 0
% 0.22/0.36 % Clauses deleted for lack of memory : 0
% 0.22/0.36 % Backward-subsumed : 0
% 0.22/0.36 % Backward-rewritten : 8
% 0.22/0.36 % Generated clauses : 526
% 0.22/0.36 % ...of the previous two non-redundant : 311
% 0.22/0.36 % ...aggressively subsumed : 0
% 0.22/0.36 % Contextual simplify-reflections : 0
% 0.22/0.36 % Paramodulations : 526
% 0.22/0.36 % Factorizations : 0
% 0.22/0.36 % NegExts : 0
% 0.22/0.36 % Equation resolutions : 0
% 0.22/0.36 % Disequality decompositions : 0
% 0.22/0.36 % Total rewrite steps : 510
% 0.22/0.36 % ...of those cached : 322
% 0.22/0.36 % Propositional unsat checks : 0
% 0.22/0.36 % Propositional check models : 0
% 0.22/0.36 % Propositional check unsatisfiable : 0
% 0.22/0.36 % Propositional clauses : 0
% 0.22/0.36 % Propositional clauses after purity: 0
% 0.22/0.36 % Propositional unsat core size : 0
% 0.22/0.36 % Propositional preprocessing time : 0.000
% 0.22/0.36 % Propositional encoding time : 0.000
% 0.22/0.36 % Propositional solver time : 0.000
% 0.22/0.36 % Success case prop preproc time : 0.000
% 0.22/0.36 % Success case prop encoding time : 0.000
% 0.22/0.36 % Success case prop solver time : 0.000
% 0.22/0.36 % Current number of processed clauses : 31
% 0.22/0.36 % Positive orientable unit clauses : 27
% 0.22/0.36 % Positive unorientable unit clauses: 4
% 0.22/0.36 % Negative unit clauses : 0
% 0.22/0.36 % Non-unit-clauses : 0
% 0.22/0.36 % Current number of unprocessed clauses: 251
% 0.22/0.36 % ...number of literals in the above : 251
% 0.22/0.36 % Current number of archived formulas : 0
% 0.22/0.36 % Current number of archived clauses : 20
% 0.22/0.36 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.36 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.36 % Non-unit clause-clause subsumptions : 0
% 0.22/0.36 % Unit Clause-clause subsumption calls : 3
% 0.22/0.36 % Rewrite failures with RHS unbound : 0
% 0.22/0.36 % BW rewrite match attempts : 97
% 0.22/0.36 % BW rewrite match successes : 54
% 0.22/0.36 % Condensation attempts : 0
% 0.22/0.36 % Condensation successes : 0
% 0.22/0.36 % Termbank termtop insertions : 4805
% 0.22/0.36 % Search garbage collected termcells : 481
% 0.22/0.36
% 0.22/0.36 % -------------------------------------------------
% 0.22/0.36 % User time : 0.016 s
% 0.22/0.36 % System time : 0.004 s
% 0.22/0.36 % Total time : 0.020 s
% 0.22/0.36 % Maximum resident set size: 3584 pages
% 0.22/0.36
% 0.22/0.36 % -------------------------------------------------
% 0.22/0.36 % User time : 0.051 s
% 0.22/0.36 % System time : 0.014 s
% 0.22/0.36 % Total time : 0.065 s
% 0.22/0.36 % Maximum resident set size: 4864 pages
% 0.22/0.36 % E exiting
%------------------------------------------------------------------------------