%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG277^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 44 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 168 ( 4 ~; 0 |; 11 &; 150 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 16 ^; 57 !; 5 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
g: $tType ).
thf(decl_23,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(decl_24,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(decl_25,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(decl_26,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(decl_27,type,
esk1_0: g > g > g ).
thf(decl_28,type,
esk2_0: g ).
thf(decl_29,type,
esk3_1: g > g ).
thf(decl_30,type,
esk4_0: g ).
thf(cGROUP3_def,axiom,
( cGROUP3
= ( ^ [X1: g > g > g,X5: g] :
( ( cGRP_ASSOC @ X1 )
& ( cGRP_RIGHT_UNIT @ X1 @ X5 )
& ( cGRP_RIGHT_INVERSE @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vuXjIUOEZn/E---3.1_3694632.p',cGROUP3_def) ).
thf(cGRP_ASSOC_def,axiom,
( cGRP_ASSOC
= ( ^ [X1: g > g > g] :
! [X2: g,X3: g,X4: g] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vuXjIUOEZn/E---3.1_3694632.p',cGRP_ASSOC_def) ).
thf(cGRP_RIGHT_INVERSE_def,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
? [X3: g] :
( ( X1 @ X2 @ X3 )
= X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vuXjIUOEZn/E---3.1_3694632.p',cGRP_RIGHT_INVERSE_def) ).
thf(cGRP_RIGHT_UNIT_def,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
( ( X1 @ X2 @ X5 )
= X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vuXjIUOEZn/E---3.1_3694632.p',cGRP_RIGHT_UNIT_def) ).
thf(cE13A2,conjecture,
! [X1: g > g > g,X5: g] :
( ( cGROUP3 @ X1 @ X5 )
=> ! [X2: g] :
( ( X1 @ X5 @ X2 )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.vuXjIUOEZn/E---3.1_3694632.p',cE13A2) ).
thf(c_0_5,plain,
( cGROUP3
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X9: g,X10: g,X11: g] :
( ( Z0 @ ( Z0 @ X9 @ X10 ) @ X11 )
= ( Z0 @ X9 @ ( Z0 @ X10 @ X11 ) ) )
& ! [X12: g] :
( ( Z0 @ X12 @ Z1 )
= X12 )
& ! [X13: g] :
? [X14: g] :
( ( Z0 @ X13 @ X14 )
= Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cGROUP3_def]) ).
thf(c_0_6,plain,
( cGRP_ASSOC
= ( ^ [Z0: g > g > g] :
! [X2: g,X3: g,X4: g] :
( ( Z0 @ ( Z0 @ X2 @ X3 ) @ X4 )
= ( Z0 @ X2 @ ( Z0 @ X3 @ X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_ASSOC_def]) ).
thf(c_0_7,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
? [X3: g] :
( ( Z0 @ X2 @ X3 )
= Z1 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_RIGHT_INVERSE_def]) ).
thf(c_0_8,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
( ( Z0 @ X2 @ Z1 )
= X2 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_RIGHT_UNIT_def]) ).
thf(c_0_9,negated_conjecture,
~ ! [X1: g > g > g,X5: g] :
( ( cGROUP3 @ X1 @ X5 )
=> ! [X2: g] :
( ( X1 @ X5 @ X2 )
= X2 ) ),
inference(assume_negation,[status(cth)],[cE13A2]) ).
thf(c_0_10,plain,
( cGROUP3
= ( ^ [Z0: g > g > g,Z1: g] :
( ! [X9: g,X10: g,X11: g] :
( ( Z0 @ ( Z0 @ X9 @ X10 ) @ X11 )
= ( Z0 @ X9 @ ( Z0 @ X10 @ X11 ) ) )
& ! [X12: g] :
( ( Z0 @ X12 @ Z1 )
= X12 )
& ! [X13: g] :
? [X14: g] :
( ( Z0 @ X13 @ X14 )
= Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_7]),c_0_8]) ).
thf(c_0_11,negated_conjecture,
~ ! [X1: g > g > g,X5: g] :
( ( ! [X15: g,X16: g,X17: g] :
( ( X1 @ ( X1 @ X15 @ X16 ) @ X17 )
= ( X1 @ X15 @ ( X1 @ X16 @ X17 ) ) )
& ! [X18: g] :
( ( X1 @ X18 @ X5 )
= X18 )
& ! [X19: g] :
? [X20: g] :
( ( X1 @ X19 @ X20 )
= X5 ) )
=> ! [X2: g] :
( ( X1 @ X5 @ X2 )
= X2 ) ),
inference(apply_def,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X23: g,X24: g,X25: g,X26: g,X27: g] :
( ( ( esk1_0 @ ( esk1_0 @ X23 @ X24 ) @ X25 )
= ( esk1_0 @ X23 @ ( esk1_0 @ X24 @ X25 ) ) )
& ( ( esk1_0 @ X26 @ esk2_0 )
= X26 )
& ( ( esk1_0 @ X27 @ ( esk3_1 @ X27 ) )
= esk2_0 )
& ( ( esk1_0 @ esk2_0 @ esk4_0 )
!= esk4_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_11])])])])]) ).
thf(c_0_13,negated_conjecture,
! [X2: g,X3: g,X4: g] :
( ( esk1_0 @ ( esk1_0 @ X2 @ X3 ) @ X4 )
= ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ esk2_0 )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ ( esk3_1 @ X2 ) )
= esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ esk2_0 @ X3 ) )
= ( esk1_0 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ ( esk3_1 @ ( esk1_0 @ X2 @ X3 ) ) ) )
= esk2_0 ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
thf(c_0_18,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ ( esk3_1 @ X2 ) @ X3 ) )
= ( esk1_0 @ esk2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X3: g,X2: g] :
( ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ ( esk3_1 @ ( esk1_0 @ esk2_0 @ X3 ) ) ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).
thf(c_0_20,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk2_0 @ ( esk3_1 @ ( esk1_0 @ esk2_0 @ ( esk3_1 @ X2 ) ) ) )
= X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk2_0 @ ( esk3_1 @ ( esk3_1 @ X2 ) ) )
= X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_14]) ).
thf(c_0_22,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk2_0 @ ( esk3_1 @ X2 ) )
= ( esk3_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_23,negated_conjecture,
! [X2: g] :
( ( esk3_1 @ ( esk3_1 @ X2 ) )
= X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_22]),c_0_22]) ).
thf(c_0_24,negated_conjecture,
( ( esk1_0 @ esk2_0 @ esk4_0 )
!= esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_25,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk2_0 @ X2 )
= X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG277^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:34:10 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.vuXjIUOEZn/E---3.1_3694632.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSMSSSLSNHSA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting post_as_ho12 with 1500s (5) cores
% 0.08/0.26 % Starting post_as_ho4 with 300s (1) cores
% 0.08/0.26 % Starting lpo8_s with 300s (1) cores
% 0.08/0.26 % Starting sh5l with 300s (1) cores
% 0.08/0.26 % post_as_ho12 with pid 3694665 completed with status 0
% 0.08/0.26 % Result found by post_as_ho12
% 0.08/0.26 % Preprocessing class: HSSSSMSSSLSNHSA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting post_as_ho12 with 1500s (5) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HUUPS-FFSF11-SHSFMFNN
% 0.08/0.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.26 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.26 % Starting post_as_ho12 with 151s (1) cores
% 0.08/0.26 % Starting sh5l with 136s (1) cores
% 0.08/0.26 % Starting new_bool_1 with 136s (1) cores
% 0.08/0.26 % Starting new_bool_2 with 136s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 3694669 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSMSSSLSNHSA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting post_as_ho12 with 1500s (5) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HUUPS-FFSF11-SHSFMFNN
% 0.08/0.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.26 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26 % Parsed axioms : 10
% 0.08/0.26 % Removed by relevancy pruning/SinE : 0
% 0.08/0.26 % Initial clauses : 9
% 0.08/0.26 % Removed in clause preprocessing : 5
% 0.08/0.26 % Initial clauses in saturation : 4
% 0.08/0.26 % Processed clauses : 18
% 0.08/0.26 % ...of these trivial : 2
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 16
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 0
% 0.08/0.26 % Backward-rewritten : 7
% 0.08/0.26 % Generated clauses : 93
% 0.08/0.26 % ...of the previous two non-redundant : 40
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 93
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 128
% 0.08/0.26 % ...of those cached : 73
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 9
% 0.08/0.26 % Positive orientable unit clauses : 9
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 0
% 0.08/0.26 % Non-unit-clauses : 0
% 0.08/0.26 % Current number of unprocessed clauses: 24
% 0.08/0.26 % ...number of literals in the above : 24
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 7
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.26 % Non-unit clause-clause subsumptions : 0
% 0.08/0.26 % Unit Clause-clause subsumption calls : 0
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 9
% 0.08/0.26 % BW rewrite match successes : 6
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 1411
% 0.08/0.26 % Search garbage collected termcells : 179
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.004 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.006 s
% 0.08/0.26 % Maximum resident set size: 3636 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.011 s
% 0.08/0.26 % System time : 0.010 s
% 0.08/0.26 % Total time : 0.021 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------