%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG278^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 07:44:59 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 140 ( 4 ~; 0 |; 11 &; 122 @)
% ( 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 : 71 ( 16 ^; 50 !; 5 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
g: $tType ).
thf(decl_23,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(decl_24,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(decl_25,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(decl_26,type,
cGRP_LEFT_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(cGROUP2_def,axiom,
( cGROUP2
= ( ^ [X1: g > g > g,X5: g] :
( ( cGRP_ASSOC @ X1 )
& ( cGRP_LEFT_UNIT @ X1 @ X5 )
& ( cGRP_LEFT_INVERSE @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.s6EP8Ir7Yi/E---3.1_3186010.p',cGROUP2_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/sandbox2/tmp/tmp.s6EP8Ir7Yi/E---3.1_3186010.p',cGRP_ASSOC_def) ).
thf(cGRP_LEFT_UNIT_def,axiom,
( cGRP_LEFT_UNIT
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
( ( X1 @ X5 @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.s6EP8Ir7Yi/E---3.1_3186010.p',cGRP_LEFT_UNIT_def) ).
thf(cGRP_LEFT_INVERSE_def,axiom,
( cGRP_LEFT_INVERSE
= ( ^ [X1: g > g > g,X5: g] :
! [X2: g] :
? [X3: g] :
( ( X1 @ X3 @ X2 )
= X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.s6EP8Ir7Yi/E---3.1_3186010.p',cGRP_LEFT_INVERSE_def) ).
thf(cE12A1,conjecture,
! [X1: g > g > g,X5: g] :
( ( cGROUP2 @ X1 @ X5 )
=> ! [X2: g] :
( ( X1 @ X2 @ X5 )
= X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.s6EP8Ir7Yi/E---3.1_3186010.p',cE12A1) ).
thf(c_0_5,plain,
( cGROUP2
= ( ^ [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 @ Z1 @ X12 )
= X12 )
& ! [X13: g] :
? [X14: g] :
( ( Z0 @ X14 @ X13 )
= Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cGROUP2_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_LEFT_UNIT
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
( ( Z0 @ Z1 @ X2 )
= X2 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_LEFT_UNIT_def]) ).
thf(c_0_8,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Z0: g > g > g,Z1: g] :
! [X2: g] :
? [X3: g] :
( ( Z0 @ X3 @ X2 )
= Z1 ) ) ),
inference(fof_simplification,[status(thm)],[cGRP_LEFT_INVERSE_def]) ).
thf(c_0_9,negated_conjecture,
~ ! [X1: g > g > g,X5: g] :
( ( cGROUP2 @ X1 @ X5 )
=> ! [X2: g] :
( ( X1 @ X2 @ X5 )
= X2 ) ),
inference(assume_negation,[status(cth)],[cE12A1]) ).
thf(c_0_10,plain,
( cGROUP2
= ( ^ [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 @ Z1 @ X12 )
= X12 )
& ! [X13: g] :
? [X14: g] :
( ( Z0 @ X14 @ X13 )
= 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 @ X5 @ X18 )
= X18 )
& ! [X19: g] :
? [X20: g] :
( ( X1 @ X20 @ X19 )
= X5 ) )
=> ! [X2: g] :
( ( X1 @ X2 @ X5 )
= 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 @ esk2_0 @ X26 )
= X26 )
& ( ( esk1_0 @ ( esk3_1 @ X27 ) @ X27 )
= esk2_0 )
& ( ( esk1_0 @ esk4_0 @ esk2_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 @ ( esk3_1 @ X2 ) @ X2 )
= esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ esk2_0 @ X2 )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ ( esk3_1 @ X2 ) @ ( esk1_0 @ X2 @ X3 ) )
= X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ ( esk3_1 @ ( esk3_1 @ X2 ) ) @ esk2_0 )
= X2 ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X2: g,X3: g] :
( ( esk1_0 @ ( esk3_1 @ ( esk3_1 @ X2 ) ) @ X3 )
= ( esk1_0 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
thf(c_0_19,negated_conjecture,
( ( esk1_0 @ esk4_0 @ esk2_0 )
!= esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_20,negated_conjecture,
! [X2: g] :
( ( esk1_0 @ X2 @ esk2_0 )
= X2 ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG278^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n010.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 17:36:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.s6EP8Ir7Yi/E---3.1_3186010.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLSNHSA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting post_as_ho12 with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho4 with 300s (1) cores
% 0.08/0.25 % Starting lpo8_s with 300s (1) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % sh5l with pid 3186026 completed with status 0
% 0.08/0.25 % Result found by sh5l
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLSNHSA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting post_as_ho12 with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho4 with 300s (1) cores
% 0.08/0.25 % Starting lpo8_s with 300s (1) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.25 % Search class: HUUPS-FFSF11-SHSFMFNN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 3186027 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLSNHSA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting post_as_ho12 with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho4 with 300s (1) cores
% 0.08/0.25 % Starting lpo8_s with 300s (1) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.25 % Search class: HUUPS-FFSF11-SHSFMFNN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 10
% 0.08/0.25 % Removed by relevancy pruning/SinE : 5
% 0.08/0.25 % Initial clauses : 4
% 0.08/0.25 % Removed in clause preprocessing : 0
% 0.08/0.25 % Initial clauses in saturation : 4
% 0.08/0.25 % Processed clauses : 12
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 12
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 5
% 0.08/0.25 % Generated clauses : 35
% 0.08/0.25 % ...of the previous two non-redundant : 15
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 35
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 40
% 0.08/0.25 % ...of those cached : 18
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 7
% 0.08/0.25 % Positive orientable unit clauses : 7
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 0
% 0.08/0.25 % Non-unit-clauses : 0
% 0.08/0.25 % Current number of unprocessed clauses: 6
% 0.08/0.25 % ...number of literals in the above : 6
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 5
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.25 % Non-unit clause-clause subsumptions : 0
% 0.08/0.25 % Unit Clause-clause subsumption calls : 0
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 8
% 0.08/0.25 % BW rewrite match successes : 5
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 752
% 0.08/0.25 % Search garbage collected termcells : 180
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.004 s
% 0.08/0.25 % System time : 0.000 s
% 0.08/0.25 % Total time : 0.004 s
% 0.08/0.25 % Maximum resident set size: 3636 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.006 s
% 0.08/0.25 % System time : 0.005 s
% 0.08/0.25 % Total time : 0.010 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------