%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG285^5 : 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 : n013.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 07:44:51 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 35 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 172 ( 10 ~; 5 |; 11 &; 144 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 50 !; 4 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
cP: a > a > a ).
thf(decl_24,type,
cE: a ).
thf(decl_25,type,
cJ: a > a ).
thf(decl_26,type,
esk1_0: a ).
thf(decl_27,type,
esk2_0: a ).
thf(decl_28,type,
esk3_0: a ).
thf(decl_29,type,
esk4_0: a ).
thf(decl_30,type,
esk5_0: a ).
thf(cTHM22_pme,conjecture,
( ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: a] :
( ( cP @ ( cJ @ X2 ) @ X2 )
= cE ) )
=> ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
& ! [X4: a,X5: a] :
( ? [X6: a] :
( ( cP @ X4 @ X6 )
= X5 )
& ? [X7: a] :
( ( cP @ X7 @ X4 )
= X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.04QSkmf4KN/E---3.1_2421571.p',cTHM22_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: a] :
( ( cP @ ( cJ @ X2 ) @ X2 )
= cE ) )
=> ( ! [X1: a,X2: a,X3: a] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
& ! [X4: a,X5: a] :
( ? [X6: a] :
( ( cP @ X4 @ X6 )
= X5 )
& ? [X7: a] :
( ( cP @ X7 @ X4 )
= X5 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM22_pme]) ).
thf(c_0_2,negated_conjecture,
! [X20: a,X21: a,X22: a,X23: a,X24: a,X30: a,X31: a] :
( ( ( cP @ ( cP @ X20 @ X21 ) @ X22 )
= ( cP @ X20 @ ( cP @ X21 @ X22 ) ) )
& ( ( cP @ cE @ X23 )
= X23 )
& ( ( cP @ ( cJ @ X24 ) @ X24 )
= cE )
& ( ( ( cP @ ( cP @ esk1_0 @ esk2_0 ) @ esk3_0 )
!= ( cP @ esk1_0 @ ( cP @ esk2_0 @ esk3_0 ) ) )
| ( ( cP @ esk4_0 @ X30 )
!= esk5_0 )
| ( ( cP @ X31 @ 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,
! [X1: a,X2: a,X3: a] :
( ( 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: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
! [X1: a,X2: a] :
( ( 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: a] :
( ( cP @ ( cJ @ ( cJ @ X1 ) ) @ cE )
= X1 ),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
thf(c_0_8,negated_conjecture,
! [X1: a] :
( ( cP @ ( cJ @ ( cJ @ ( cJ @ X1 ) ) ) @ X1 )
= cE ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: a] :
( ( cJ @ ( cJ @ X1 ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_8]),c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: a,X2: a] :
( ( ( cP @ ( cP @ esk1_0 @ esk2_0 ) @ esk3_0 )
!= ( cP @ esk1_0 @ ( cP @ esk2_0 @ esk3_0 ) ) )
| ( ( cP @ esk4_0 @ X1 )
!= esk5_0 )
| ( ( cP @ X2 @ esk4_0 )
!= esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_11,negated_conjecture,
! [X1: a,X2: a,X3: a] :
( ( cP @ ( cJ @ ( cP @ X1 @ X2 ) ) @ ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
= X3 ),
inference(spm,[status(thm)],[c_0_6,c_0_3]) ).
thf(c_0_12,negated_conjecture,
! [X1: a] :
( ( cP @ X1 @ cE )
= X1 ),
inference(rw,[status(thm)],[c_0_7,c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X1: a,X2: a] :
( ( ( cP @ X1 @ esk4_0 )
!= esk5_0 )
| ( ( cP @ esk4_0 @ X2 )
!= esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_3])]) ).
thf(c_0_14,negated_conjecture,
! [X1: a,X2: a] :
( ( cP @ ( cJ @ ( cP @ X1 @ ( cJ @ X2 ) ) ) @ X1 )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_4]),c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X1: a] :
( ( cP @ esk4_0 @ X1 )
!= esk5_0 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14])]) ).
thf(c_0_16,negated_conjecture,
! [X1: a,X2: a] :
( ( cP @ X1 @ ( cP @ ( cJ @ X1 ) @ X2 ) )
= X2 ),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG285^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.15 % Computer : n013.cluster.edu
% 0.07/0.15 % Model : x86_64 x86_64
% 0.07/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.15 % Memory : 8046.5625MB
% 0.07/0.15 % OS : Linux 6.8.0-71-generic
% 0.07/0.15 % CPULimit : 300
% 0.07/0.15 % WCLimit : 300
% 0.07/0.15 % DateTime : Tue Sep 29 17:37:06 UTC 2026
% 0.07/0.16 % CPUTime :
% 0.07/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.21 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.04QSkmf4KN/E---3.1_2421571.p
% 0.07/0.23 % Version: 3.5.1-ho
% 0.07/0.23 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.23 % Starting sh4l with 300s (1) cores
% 0.07/0.23 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.07/0.23 % ho_unfolding_6 with pid 2421585 completed with status 0
% 0.07/0.23 % Result found by ho_unfolding_6
% 0.07/0.23 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.23 % No SInE strategy applied
% 0.07/0.23 % Search class: HUHPS-FFSF21-SFFFFFNN
% 0.07/0.23 % partial match(1): HUUPS-FFSF21-SFFFFFNN
% 0.07/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.23 % SubtermCWHack with pid 2421588 completed with status 0
% 0.07/0.23 % Result found by SubtermCWHack
% 0.07/0.23 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.23 % No SInE strategy applied
% 0.07/0.23 % Search class: HUHPS-FFSF21-SFFFFFNN
% 0.07/0.23 % partial match(1): HUUPS-FFSF21-SFFFFFNN
% 0.07/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.23 % Preprocessing time : 0.001 s
% 0.07/0.23
% 0.07/0.23 % Proof found!
% 0.07/0.23 % SZS status Theorem
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23 % Parsed axioms : 5
% 0.07/0.23 % Removed by relevancy pruning/SinE : 0
% 0.07/0.23 % Initial clauses : 8
% 0.07/0.23 % Removed in clause preprocessing : 4
% 0.07/0.23 % Initial clauses in saturation : 4
% 0.07/0.23 % Processed clauses : 26
% 0.07/0.23 % ...of these trivial : 2
% 0.07/0.23 % ...subsumed : 0
% 0.07/0.23 % ...remaining for further processing : 24
% 0.07/0.23 % Other redundant clauses eliminated : 4
% 0.07/0.23 % Clauses deleted for lack of memory : 0
% 0.07/0.23 % Backward-subsumed : 3
% 0.07/0.23 % Backward-rewritten : 6
% 0.07/0.23 % Generated clauses : 162
% 0.07/0.23 % ...of the previous two non-redundant : 72
% 0.07/0.23 % ...aggressively subsumed : 0
% 0.07/0.23 % Contextual simplify-reflections : 0
% 0.07/0.23 % Paramodulations : 158
% 0.07/0.23 % Factorizations : 0
% 0.07/0.23 % NegExts : 0
% 0.07/0.23 % Equation resolutions : 4
% 0.07/0.23 % Disequality decompositions : 0
% 0.07/0.23 % Total rewrite steps : 220
% 0.07/0.23 % ...of those cached : 164
% 0.07/0.23 % Propositional unsat checks : 0
% 0.07/0.23 % Propositional check models : 0
% 0.07/0.23 % Propositional check unsatisfiable : 0
% 0.07/0.23 % Propositional clauses : 0
% 0.07/0.23 % Propositional clauses after purity: 0
% 0.07/0.23 % Propositional unsat core size : 0
% 0.07/0.23 % Propositional preprocessing time : 0.000
% 0.07/0.23 % Propositional encoding time : 0.000
% 0.07/0.23 % Propositional solver time : 0.000
% 0.07/0.23 % Success case prop preproc time : 0.000
% 0.07/0.23 % Success case prop encoding time : 0.000
% 0.07/0.23 % Success case prop solver time : 0.000
% 0.07/0.23 % Current number of processed clauses : 15
% 0.07/0.23 % Positive orientable unit clauses : 12
% 0.07/0.23 % Positive unorientable unit clauses: 0
% 0.07/0.23 % Negative unit clauses : 3
% 0.07/0.23 % Non-unit-clauses : 0
% 0.07/0.23 % Current number of unprocessed clauses: 40
% 0.07/0.23 % ...number of literals in the above : 41
% 0.07/0.23 % Current number of archived formulas : 0
% 0.07/0.23 % Current number of archived clauses : 9
% 0.07/0.23 % Clause-clause subsumption calls (NU) : 2
% 0.07/0.23 % Rec. Clause-clause subsumption calls : 2
% 0.07/0.23 % Non-unit clause-clause subsumptions : 0
% 0.07/0.23 % Unit Clause-clause subsumption calls : 5
% 0.07/0.23 % Rewrite failures with RHS unbound : 0
% 0.07/0.23 % BW rewrite match attempts : 11
% 0.07/0.23 % BW rewrite match successes : 6
% 0.07/0.23 % Condensation attempts : 0
% 0.07/0.23 % Condensation successes : 0
% 0.07/0.23 % Termbank termtop insertions : 1638
% 0.07/0.23 % Search garbage collected termcells : 157
% 0.07/0.23
% 0.07/0.23 % -------------------------------------------------
% 0.07/0.23 % User time : 0.006 s
% 0.07/0.23 % System time : 0.000 s
% 0.07/0.23 % Total time : 0.006 s
% 0.07/0.23 % Maximum resident set size: 3632 pages
% 0.07/0.23
% 0.07/0.23 % -------------------------------------------------
% 0.07/0.23 % User time : 0.007 s
% 0.07/0.23 % System time : 0.005 s
% 0.07/0.23 % Total time : 0.012 s
% 0.07/0.23 % Maximum resident set size: 4864 pages
% 0.07/0.23 % E exiting
%------------------------------------------------------------------------------