%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA125^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 07:45:36 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 100 ( 9 ~; 2 |; 1 &; 83 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 12 ^; 24 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
'type/realax/real': $tType ).
thf(decl_23,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(decl_24,type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(decl_25,type,
esk1_0: 'type/realax/real' > 'type/realax/real' ).
thf(decl_26,type,
esk2_0: 'type/realax/real' ).
thf(decl_29,type,
esk5_1: 'type/realax/real' > 'type/realax/real' ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_RMUL_',conjecture,
! [X1: 'type/realax/real' > 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X1 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X3: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X1 @ X3 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.stChiaCskW/E---3.1_1629735.p','thm/iterate/POLYNOMIAL_FUNCTION_RMUL_') ).
thf('thm/iterate/POLYNOMIAL_FUNCTION_LMUL_',axiom,
! [X1: 'type/realax/real' > 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X1 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X3: 'type/realax/real'] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.stChiaCskW/E---3.1_1629735.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_') ).
thf('thm/realax/REAL_MUL_SYM_',axiom,
! [X4: 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X4 @ X2 )
= ( 'const/realax/real_mul' @ X2 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.stChiaCskW/E---3.1_1629735.p','thm/realax/REAL_MUL_SYM_') ).
thf(c_0_3,negated_conjecture,
~ ! [X1: 'type/realax/real' > 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X1 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X3: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X1 @ X3 ) @ X2 ) ) ),
inference(assume_negation,[status(cth)],['thm/iterate/POLYNOMIAL_FUNCTION_RMUL_']) ).
thf(c_0_4,plain,
! [X1: 'type/realax/real' > 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X1 )
=> ( 'const/iterate/polynomial_function'
@ ^ [Z0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],['thm/iterate/POLYNOMIAL_FUNCTION_LMUL_']) ).
thf(c_0_5,negated_conjecture,
~ ! [X1: 'type/realax/real' > 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X1 )
=> ( 'const/iterate/polynomial_function'
@ ^ [Z0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X1 @ Z0 ) @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
thf(c_0_6,plain,
! [X11: 'type/realax/real' > 'type/realax/real',X12: 'type/realax/real'] :
( ~ ( 'const/iterate/polynomial_function' @ X11 )
| ( 'const/iterate/polynomial_function'
@ ^ [Z0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X12 @ ( X11 @ Z0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
thf(c_0_7,negated_conjecture,
( ( 'const/iterate/polynomial_function' @ esk1_0 )
& ~ ( 'const/iterate/polynomial_function'
@ ^ [Z0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( esk1_0 @ Z0 ) @ esk2_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
thf(c_0_8,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( 'const/iterate/polynomial_function'
@ ^ [Z0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ Z0 ) ) )
| ~ ( 'const/iterate/polynomial_function' @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
'const/iterate/polynomial_function' @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ( 'const/iterate/polynomial_function'
@ ^ [Z0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( esk1_0 @ Z0 ) @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X2: 'type/realax/real'] :
( 'const/iterate/polynomial_function'
@ ^ [Z0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X2 @ ( esk1_0 @ Z0 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,plain,
! [X2: 'type/realax/real'] :
( ( ^ [Z0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( esk1_0 @ Z0 ) @ esk2_0 ) )
!= ( ^ [Z0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X2 @ ( esk1_0 @ Z0 ) ) ) ),
inference(ext_sup,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_13,plain,
! [X13: 'type/realax/real',X14: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X13 @ X14 )
= ( 'const/realax/real_mul' @ X14 @ X13 ) ),
inference(variable_rename,[status(thm)],['thm/realax/REAL_MUL_SYM_']) ).
thf(c_0_14,plain,
! [X2: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( esk1_0 @ ( esk5_1 @ X2 ) ) @ esk2_0 )
!= ( 'const/realax/real_mul' @ X2 @ ( esk1_0 @ ( esk5_1 @ X2 ) ) ) ),
inference(neg_ext,[status(thm)],[c_0_12]) ).
thf(c_0_15,plain,
! [X3: 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X2 @ X3 )
= ( 'const/realax/real_mul' @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,plain,
! [X2: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ esk2_0 @ ( esk1_0 @ ( esk5_1 @ X2 ) ) )
!= ( 'const/realax/real_mul' @ X2 @ ( esk1_0 @ ( esk5_1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_17,plain,
$false,
inference(er,[status(thm)],[c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA125^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:47:28 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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.stChiaCskW/E---3.1_1629735.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting sh3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.26 % Starting sh2lt with 300s (1) cores
% 0.09/0.26 % Starting ho_unfolding_1 with 300s (1) cores
% 0.09/0.26 % ho_unfolding_1 with pid 1629767 completed with status 0
% 0.09/0.26 % Result found by ho_unfolding_1
% 0.09/0.26 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting sh3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.26 % Starting sh2lt with 300s (1) cores
% 0.09/0.26 % Starting ho_unfolding_1 with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HHUSF-FFSF22-MSSFFFNN
% 0.09/0.26 % partial match(1): HHUSF-FFSF22-SSSFFFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 1629769 completed with status 10
% 0.09/0.26 % Starting ho_unfolding_1 with 31s (1) cores
% 0.09/0.26 % ho_unfolding_1 with pid 1629777 completed with status 0
% 0.09/0.26 % Result found by ho_unfolding_1
% 0.09/0.26 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting sh3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.26 % Starting sh2lt with 300s (1) cores
% 0.09/0.26 % Starting ho_unfolding_1 with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HHUSF-FFSF22-MSSFFFNN
% 0.09/0.26 % partial match(1): HHUSF-FFSF22-SSSFFFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 1629769 completed with status 10
% 0.09/0.26 % Starting ho_unfolding_1 with 31s (1) cores
% 0.09/0.26 % Preprocessing time : 0.001 s
% 0.09/0.26 % Presaturation interreduction done
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26 % Parsed axioms : 6
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 7
% 0.09/0.26 % Removed in clause preprocessing : 3
% 0.09/0.26 % Initial clauses in saturation : 4
% 0.09/0.26 % Processed clauses : 16
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 0
% 0.09/0.26 % ...remaining for further processing : 16
% 0.09/0.26 % Other redundant clauses eliminated : 0
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 0
% 0.09/0.26 % Backward-rewritten : 0
% 0.09/0.26 % Generated clauses : 17
% 0.09/0.26 % ...of the previous two non-redundant : 14
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 10
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 3
% 0.09/0.26 % Equation resolutions : 1
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 0
% 0.09/0.26 % ...of those cached : 0
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 12
% 0.09/0.26 % Positive orientable unit clauses : 2
% 0.09/0.26 % Positive unorientable unit clauses: 1
% 0.09/0.26 % Negative unit clauses : 6
% 0.09/0.26 % Non-unit-clauses : 3
% 0.09/0.26 % Current number of unprocessed clauses: 6
% 0.09/0.26 % ...number of literals in the above : 10
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 4
% 0.27/0.26 % Clause-clause subsumption calls (NU) : 1
% 0.27/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.27/0.26 % Non-unit clause-clause subsumptions : 0
% 0.27/0.26 % Unit Clause-clause subsumption calls : 4
% 0.27/0.26 % Rewrite failures with RHS unbound : 0
% 0.27/0.26 % BW rewrite match attempts : 0
% 0.27/0.26 % BW rewrite match successes : 0
% 0.27/0.26 % Condensation attempts : 16
% 0.27/0.26 % Condensation successes : 0
% 0.27/0.26 % Termbank termtop insertions : 642
% 0.27/0.26 % Search garbage collected termcells : 67
% 0.27/0.26
% 0.27/0.26 % -------------------------------------------------
% 0.27/0.26 % User time : 0.003 s
% 0.27/0.26 % System time : 0.003 s
% 0.27/0.26 % Total time : 0.006 s
% 0.27/0.26 % Maximum resident set size: 3888 pages
% 0.27/0.26
% 0.27/0.26 % -------------------------------------------------
% 0.27/0.26 % User time : 0.007 s
% 0.27/0.26 % System time : 0.005 s
% 0.27/0.26 % Total time : 0.012 s
% 0.27/0.26 % Maximum resident set size: 4864 pages
% 0.27/0.26 % E exiting
%------------------------------------------------------------------------------