%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU930^5 : 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 : n001.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 08:25:58 AM UTC 2026
% Result : Theorem 0.27s 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 27 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 65 ( 6 ~; 2 |; 6 &; 42 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 10 ^; 9 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
f: $i > $i ).
thf(decl_24,type,
g: $i > $i ).
thf(decl_25,type,
esk1_0: $i ).
thf(cTHM171A_pme,conjecture,
( ( ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) )
= ( ^ [X1: $i] : ( g @ ( f @ X1 ) ) ) )
=> ! [X1: $i] :
( ( ( ( g @ X1 )
= X1 )
& ! [X2: $i] :
( ( ( g @ X2 )
= X2 )
=> ( X2 = X1 ) ) )
=> ( ( f @ X1 )
= X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RqwmpPVVu9/E---3.1_1345488.p',cTHM171A_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ( ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) )
= ( ^ [X1: $i] : ( g @ ( f @ X1 ) ) ) )
=> ! [X1: $i] :
( ( ( ( g @ X1 )
= X1 )
& ! [X2: $i] :
( ( ( g @ X2 )
= X2 )
=> ( X2 = X1 ) ) )
=> ( ( f @ X1 )
= X1 ) ) ),
inference(assume_negation,[status(cth)],[cTHM171A_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ( ( ^ [Z0: $i] : ( f @ ( g @ Z0 ) ) )
= ( ^ [Z0: $i] : ( g @ ( f @ Z0 ) ) ) )
=> ! [X1: $i] :
( ( ( ( g @ X1 )
= X1 )
& ! [X2: $i] :
( ( ( g @ X2 )
= X2 )
=> ( X2 = X1 ) ) )
=> ( ( f @ X1 )
= X1 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X6: $i] :
( ( ( ^ [Z0: $i] : ( f @ ( g @ Z0 ) ) )
= ( ^ [Z0: $i] : ( g @ ( f @ Z0 ) ) ) )
& ( ( g @ esk1_0 )
= esk1_0 )
& ( ( ( g @ X6 )
!= X6 )
| ( X6 = esk1_0 ) )
& ( ( f @ esk1_0 )
!= esk1_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_2])])])])]) ).
thf(c_0_4,negated_conjecture,
( ( ^ [Z0: $i] : ( f @ ( g @ Z0 ) ) )
= ( ^ [Z0: $i] : ( g @ ( f @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X1: $i] :
( ( f @ ( g @ X1 ) )
= ( g @ ( f @ X1 ) ) ),
inference(arg_cong,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
( ( g @ esk1_0 )
= esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i] :
( ( X1 = esk1_0 )
| ( ( g @ X1 )
!= X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
( ( g @ ( f @ esk1_0 ) )
= ( f @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_9,negated_conjecture,
( ( f @ esk1_0 )
!= esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_10,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU930^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:52:50 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.RqwmpPVVu9/E---3.1_1345488.p
% 0.27/0.26 % Version: 3.5.1-ho
% 0.27/0.26 % Preprocessing class: HSSSSMSSSSSNSSN.
% 0.27/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.26 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.27/0.26 % Starting post_as_ho10 with 300s (1) cores
% 0.27/0.26 % Starting new_bool_9 with 300s (1) cores
% 0.27/0.26 % Starting sh5l with 300s (1) cores
% 0.27/0.26 % new_bool_9 with pid 1345503 completed with status 0
% 0.27/0.26 % Result found by new_bool_9
% 0.27/0.26 % Preprocessing class: HSSSSMSSSSSNSSN.
% 0.27/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.26 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.27/0.26 % Starting post_as_ho10 with 300s (1) cores
% 0.27/0.26 % Starting new_bool_9 with 300s (1) cores
% 0.27/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.27/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.27/0.26 % Search class: HHUPF-FFSF11-MSSFFFNN
% 0.27/0.26 % partial match(1): HHUPF-FFSF11-MSSFFMNN
% 0.27/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.26 % SubtermCWHack with pid 1345506 completed with status 0
% 0.27/0.27 % Result found by SubtermCWHack
% 0.27/0.27 % Preprocessing class: HSSSSMSSSSSNSSN.
% 0.27/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.27 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.27/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.27/0.27 % Starting new_bool_9 with 300s (1) cores
% 0.27/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.27/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.27/0.27 % Search class: HHUPF-FFSF11-MSSFFFNN
% 0.27/0.27 % partial match(1): HHUPF-FFSF11-MSSFFMNN
% 0.27/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.27 % Preprocessing time : 0.001 s
% 0.27/0.27
% 0.27/0.27 % Proof found!
% 0.27/0.27 % SZS status Theorem
% 0.27/0.27 % SZS output start CNFRefutation
% See solution above
% 0.27/0.27 % Parsed axioms : 3
% 0.27/0.27 % Removed by relevancy pruning/SinE : 2
% 0.27/0.27 % Initial clauses : 4
% 0.27/0.27 % Removed in clause preprocessing : 0
% 0.27/0.27 % Initial clauses in saturation : 4
% 0.27/0.27 % Processed clauses : 6
% 0.27/0.27 % ...of these trivial : 0
% 0.27/0.27 % ...subsumed : 0
% 0.27/0.27 % ...remaining for further processing : 6
% 0.27/0.27 % Other redundant clauses eliminated : 0
% 0.27/0.27 % Clauses deleted for lack of memory : 0
% 0.27/0.27 % Backward-subsumed : 0
% 0.27/0.27 % Backward-rewritten : 0
% 0.27/0.27 % Generated clauses : 4
% 0.27/0.27 % ...of the previous two non-redundant : 2
% 0.27/0.27 % ...aggressively subsumed : 0
% 0.27/0.27 % Contextual simplify-reflections : 0
% 0.27/0.27 % Paramodulations : 3
% 0.27/0.27 % Factorizations : 0
% 0.27/0.27 % NegExts : 0
% 0.27/0.27 % Equation resolutions : 0
% 0.27/0.27 % Disequality decompositions : 0
% 0.27/0.27 % Total rewrite steps : 0
% 0.27/0.27 % ...of those cached : 0
% 0.27/0.27 % Propositional unsat checks : 0
% 0.27/0.27 % Propositional check models : 0
% 0.27/0.27 % Propositional check unsatisfiable : 0
% 0.27/0.27 % Propositional clauses : 0
% 0.27/0.27 % Propositional clauses after purity: 0
% 0.27/0.27 % Propositional unsat core size : 0
% 0.27/0.27 % Propositional preprocessing time : 0.000
% 0.27/0.27 % Propositional encoding time : 0.000
% 0.27/0.27 % Propositional solver time : 0.000
% 0.27/0.27 % Success case prop preproc time : 0.000
% 0.27/0.27 % Success case prop encoding time : 0.000
% 0.27/0.27 % Success case prop solver time : 0.000
% 0.27/0.27 % Current number of processed clauses : 6
% 0.27/0.27 % Positive orientable unit clauses : 4
% 0.27/0.27 % Positive unorientable unit clauses: 0
% 0.27/0.27 % Negative unit clauses : 1
% 0.27/0.27 % Non-unit-clauses : 1
% 0.27/0.27 % Current number of unprocessed clauses: 0
% 0.27/0.27 % ...number of literals in the above : 0
% 0.27/0.27 % Current number of archived formulas : 0
% 0.27/0.27 % Current number of archived clauses : 0
% 0.27/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.27/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.27/0.27 % Non-unit clause-clause subsumptions : 0
% 0.27/0.27 % Unit Clause-clause subsumption calls : 0
% 0.27/0.27 % Rewrite failures with RHS unbound : 0
% 0.27/0.27 % BW rewrite match attempts : 0
% 0.27/0.27 % BW rewrite match successes : 0
% 0.27/0.27 % Condensation attempts : 0
% 0.27/0.27 % Condensation successes : 0
% 0.27/0.27 % Termbank termtop insertions : 288
% 0.27/0.27 % Search garbage collected termcells : 89
% 0.27/0.27
% 0.27/0.27 % -------------------------------------------------
% 0.27/0.27 % User time : 0.003 s
% 0.27/0.27 % System time : 0.001 s
% 0.27/0.27 % Total time : 0.004 s
% 0.27/0.27 % Maximum resident set size: 3628 pages
% 0.27/0.27
% 0.27/0.27 % -------------------------------------------------
% 0.27/0.27 % User time : 0.004 s
% 0.27/0.27 % System time : 0.006 s
% 0.27/0.27 % Total time : 0.010 s
% 0.27/0.27 % Maximum resident set size: 4608 pages
% 0.27/0.27 % E exiting
%------------------------------------------------------------------------------