%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG281^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 07:44:50 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 98 ( 3 ~; 0 |; 7 &; 86 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cE: $i ).
thf(decl_24,type,
cJ: $i > $i ).
thf(decl_25,type,
cP: $i > $i > $i ).
thf(decl_26,type,
esk1_0: $i ).
thf(cTHM16_pme,conjecture,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
& ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: $i] :
( ( cP @ ( cJ @ X2 ) @ X2 )
= cE ) )
=> ! [X4: $i] :
( ( cP @ X4 @ ( cJ @ X4 ) )
= cE ) ),
file('/export/starexec/sandbox/tmp/tmp.hVfFW7hxXu/E---3.1_3477273.p',cTHM16_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
& ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: $i] :
( ( cP @ ( cJ @ X2 ) @ X2 )
= cE ) )
=> ! [X4: $i] :
( ( cP @ X4 @ ( cJ @ X4 ) )
= cE ) ),
inference(assume_negation,[status(cth)],[cTHM16_pme]) ).
thf(c_0_2,negated_conjecture,
! [X11: $i,X12: $i,X13: $i,X14: $i,X15: $i] :
( ( ( cP @ ( cP @ X11 @ X12 ) @ X13 )
= ( cP @ X11 @ ( cP @ X12 @ X13 ) ) )
& ( ( cP @ cE @ X14 )
= X14 )
& ( ( cP @ ( cJ @ X15 ) @ X15 )
= cE )
& ( ( cP @ esk1_0 @ ( cJ @ esk1_0 ) )
!= cE ) ),
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,
! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X1: $i] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP @ ( cJ @ X1 ) @ ( cP @ X1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i] :
( ( cP @ ( cJ @ ( cJ @ X1 ) ) @ cE )
= X1 ),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP @ ( cJ @ ( cJ @ X1 ) ) @ X2 )
= ( cP @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
( ( cP @ X1 @ cE )
= X1 ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i] :
( ( cJ @ ( cJ @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ( cP @ esk1_0 @ ( cJ @ esk1_0 ) )
!= cE ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( cP @ X1 @ ( cJ @ X1 ) )
= cE ),
inference(spm,[status(thm)],[c_0_4,c_0_10]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG281^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n008.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 17:37:09 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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.hVfFW7hxXu/E---3.1_3477273.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.10/0.24 % Starting sh4l with 300s (1) cores
% 0.10/0.24 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.10/0.24 % ho_unfolding_6 with pid 3477287 completed with status 0
% 0.10/0.24 % Result found by ho_unfolding_6
% 0.10/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HUUPS-FFSF21-SFFFFFNN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.24 % SubtermCWHack with pid 3477291 completed with status 0
% 0.10/0.24 % Result found by SubtermCWHack
% 0.10/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HUUPS-FFSF21-SFFFFFNN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.24 % Preprocessing time : 0.001 s
% 0.10/0.24
% 0.10/0.24 % Proof found!
% 0.10/0.24 % SZS status Theorem
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24 % Parsed axioms : 4
% 0.10/0.24 % Removed by relevancy pruning/SinE : 0
% 0.10/0.24 % Initial clauses : 7
% 0.10/0.24 % Removed in clause preprocessing : 3
% 0.10/0.24 % Initial clauses in saturation : 4
% 0.10/0.24 % Processed clauses : 14
% 0.10/0.24 % ...of these trivial : 0
% 0.10/0.24 % ...subsumed : 0
% 0.10/0.24 % ...remaining for further processing : 14
% 0.10/0.24 % Other redundant clauses eliminated : 0
% 0.10/0.24 % Clauses deleted for lack of memory : 0
% 0.10/0.24 % Backward-subsumed : 0
% 0.10/0.24 % Backward-rewritten : 6
% 0.10/0.24 % Generated clauses : 44
% 0.10/0.24 % ...of the previous two non-redundant : 18
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 0
% 0.10/0.24 % Paramodulations : 44
% 0.10/0.24 % Factorizations : 0
% 0.10/0.24 % NegExts : 0
% 0.10/0.24 % Equation resolutions : 0
% 0.10/0.24 % Disequality decompositions : 0
% 0.10/0.24 % Total rewrite steps : 47
% 0.10/0.24 % ...of those cached : 22
% 0.10/0.24 % Propositional unsat checks : 0
% 0.10/0.24 % Propositional check models : 0
% 0.10/0.24 % Propositional check unsatisfiable : 0
% 0.10/0.24 % Propositional clauses : 0
% 0.10/0.24 % Propositional clauses after purity: 0
% 0.10/0.24 % Propositional unsat core size : 0
% 0.10/0.24 % Propositional preprocessing time : 0.000
% 0.10/0.24 % Propositional encoding time : 0.000
% 0.10/0.24 % Propositional solver time : 0.000
% 0.10/0.24 % Success case prop preproc time : 0.000
% 0.10/0.24 % Success case prop encoding time : 0.000
% 0.10/0.24 % Success case prop solver time : 0.000
% 0.10/0.24 % Current number of processed clauses : 8
% 0.10/0.24 % Positive orientable unit clauses : 8
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 0
% 0.10/0.24 % Non-unit-clauses : 0
% 0.10/0.24 % Current number of unprocessed clauses: 6
% 0.10/0.24 % ...number of literals in the above : 6
% 0.10/0.24 % Current number of archived formulas : 0
% 0.10/0.24 % Current number of archived clauses : 6
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.24 % Non-unit clause-clause subsumptions : 0
% 0.10/0.24 % Unit Clause-clause subsumption calls : 0
% 0.10/0.24 % Rewrite failures with RHS unbound : 0
% 0.10/0.24 % BW rewrite match attempts : 9
% 0.10/0.24 % BW rewrite match successes : 6
% 0.10/0.24 % Condensation attempts : 0
% 0.10/0.24 % Condensation successes : 0
% 0.10/0.24 % Termbank termtop insertions : 627
% 0.10/0.24 % Search garbage collected termcells : 100
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.002 s
% 0.10/0.24 % System time : 0.003 s
% 0.10/0.24 % Total time : 0.005 s
% 0.10/0.24 % Maximum resident set size: 3628 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.005 s
% 0.10/0.24 % System time : 0.006 s
% 0.10/0.24 % Total time : 0.011 s
% 0.10/0.24 % Maximum resident set size: 4864 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------