%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP117^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:04:24 AM UTC 2026
% Result : Theorem 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 11 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 94 ( 5 ~; 0 |; 0 &; 89 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 5 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
extend1728876344nnreal: $tType ).
thf(decl_sort2,type,
set_Fi1058188332real_n: $tType ).
thf(decl_sort3,type,
sigma_1466784463real_n: $tType ).
thf(decl_sort4,type,
nat: $tType ).
thf(decl_sort5,type,
finite964658038_int_n: $tType ).
thf(decl_32,type,
comple230862828real_n: sigma_1466784463real_n > sigma_1466784463real_n ).
thf(decl_49,type,
lebesg260170249real_n: sigma_1466784463real_n ).
thf(decl_119,type,
sigma_1536574303real_n: sigma_1466784463real_n > set_Fi1058188332real_n > extend1728876344nnreal ).
thf(decl_135,type,
t: finite964658038_int_n > set_Fi1058188332real_n ).
thf(decl_136,type,
t2: finite964658038_int_n > set_Fi1058188332real_n ).
thf(decl_137,type,
f: nat > finite964658038_int_n ).
thf(decl_138,type,
esk1_0: nat ).
thf(decl_143,type,
esk6_0: nat > set_Fi1058188332real_n ).
thf(conj_0,conjecture,
( ( ^ [X2: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X2 ) ) ) )
= ( ^ [X2: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MWDAZt4qpb/E---3.1_608223.p',conj_0) ).
thf(fact_0_emeasure__T_H,axiom,
! [X1: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ X1 ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MWDAZt4qpb/E---3.1_608223.p',fact_0_emeasure__T_H) ).
thf(c_0_2,negated_conjecture,
( ( ^ [X2: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X2 ) ) ) )
!= ( ^ [X2: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_3,negated_conjecture,
~ ! [X964: nat] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X964 ) ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X964 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2])]) ).
thf(c_0_4,negated_conjecture,
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ esk1_0 ) ) )
!= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ esk1_0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
thf(c_0_5,plain,
! [X1122: nat] :
( ( esk6_0 @ X1122 )
= ( t2 @ ( f @ X1122 ) ) ),
inference(variable_rename,[status(thm)],[]) ).
thf(c_0_6,negated_conjecture,
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ esk1_0 ) ) )
!= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ esk1_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X2: nat] :
( ( esk6_0 @ X2 )
= ( t2 @ ( f @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X971: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ X971 ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ X971 ) ) ),
inference(variable_rename,[status(thm)],[fact_0_emeasure__T_H]) ).
thf(c_0_9,negated_conjecture,
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ esk1_0 ) ) )
!= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( esk6_0 @ esk1_0 ) ) ),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,plain,
! [X1: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ X1 ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_7])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP117^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 19:55:48 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.18 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.MWDAZt4qpb/E---3.1_608223.p
% 0.08/0.21 % Version: 3.5.1-ho
% 0.08/0.21 % Preprocessing class: HSLMSMSMSSLNHSA.
% 0.08/0.21 % Scheduled 7 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.21 % Starting new_bool_8 with 600s (2) cores
% 0.08/0.21 % Starting new_ho_3 with 300s (1) cores
% 0.08/0.21 % Starting additional_ho_3 with 300s (1) cores
% 0.08/0.21 % Starting full_lambda_10 with 300s (1) cores
% 0.08/0.21 % Starting ehoh_best with 300s (1) cores
% 0.08/0.21 % Starting sh2lt with 300s (1) cores
% 0.08/0.21 % Starting full_lambda_4 with 300s (1) cores
% 0.08/0.21 % new_bool_8 with pid 608236 completed with status 0
% 0.08/0.21 % Result found by new_bool_8
% 0.08/0.21 % Preprocessing class: HSLMSMSMSSLNHSA.
% 0.08/0.21 % Scheduled 7 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.21 % Starting new_bool_8 with 600s (2) cores
% 0.08/0.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.08/0.21 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.08/0.21 % Search class: HGUSM-FFMF21-MHSFFSNN
% 0.08/0.21 % partial match(4): FGUSM-FFMF21-MFFFFFNN
% 0.08/0.21 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.08/0.21 % Starting SubtermCWHack with 55s (1) cores
% 0.08/0.21 % Starting new_bool_8 with 61s (1) cores
% 0.08/0.21 % new_bool_8 with pid 608244 completed with status 0
% 0.08/0.21 % Result found by new_bool_8
% 0.08/0.21 % Preprocessing class: HSLMSMSMSSLNHSA.
% 0.08/0.21 % Scheduled 7 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.21 % Starting new_bool_8 with 600s (2) cores
% 0.08/0.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.08/0.21 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.08/0.21 % Search class: HGUSM-FFMF21-MHSFFSNN
% 0.08/0.21 % partial match(4): FGUSM-FFMF21-MFFFFFNN
% 0.08/0.21 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.08/0.21 % Starting SubtermCWHack with 55s (1) cores
% 0.08/0.21 % Starting new_bool_8 with 61s (1) cores
% 0.08/0.21 % Preprocessing time : 0.002 s
% 0.08/0.21 % Presaturation interreduction done
% 0.08/0.21
% 0.08/0.21 % Proof found!
% 0.08/0.21 % SZS status Theorem
% 0.08/0.21 % SZS output start CNFRefutation
% See solution above
% 0.08/0.21 % Parsed axioms : 487
% 0.08/0.21 % Removed by relevancy pruning/SinE : 446
% 0.08/0.21 % Initial clauses : 56
% 0.08/0.21 % Removed in clause preprocessing : 0
% 0.08/0.21 % Initial clauses in saturation : 56
% 0.08/0.21 % Processed clauses : 3
% 0.08/0.21 % ...of these trivial : 0
% 0.08/0.21 % ...subsumed : 0
% 0.08/0.21 % ...remaining for further processing : 3
% 0.08/0.21 % Other redundant clauses eliminated : 0
% 0.08/0.21 % Clauses deleted for lack of memory : 0
% 0.08/0.21 % Backward-subsumed : 0
% 0.08/0.21 % Backward-rewritten : 1
% 0.08/0.21 % Generated clauses : 0
% 0.08/0.21 % ...of the previous two non-redundant : 0
% 0.08/0.21 % ...aggressively subsumed : 0
% 0.08/0.21 % Contextual simplify-reflections : 0
% 0.08/0.21 % Paramodulations : 0
% 0.08/0.21 % Factorizations : 0
% 0.08/0.21 % NegExts : 0
% 0.08/0.21 % Equation resolutions : 0
% 0.08/0.21 % Disequality decompositions : 0
% 0.08/0.21 % Total rewrite steps : 3
% 0.08/0.21 % ...of those cached : 1
% 0.08/0.21 % Propositional unsat checks : 0
% 0.08/0.21 % Propositional check models : 0
% 0.08/0.21 % Propositional check unsatisfiable : 0
% 0.08/0.21 % Propositional clauses : 0
% 0.08/0.21 % Propositional clauses after purity: 0
% 0.08/0.21 % Propositional unsat core size : 0
% 0.08/0.21 % Propositional preprocessing time : 0.000
% 0.08/0.21 % Propositional encoding time : 0.000
% 0.08/0.21 % Propositional solver time : 0.000
% 0.08/0.21 % Success case prop preproc time : 0.000
% 0.08/0.21 % Success case prop encoding time : 0.000
% 0.08/0.21 % Success case prop solver time : 0.000
% 0.08/0.21 % Current number of processed clauses : 2
% 0.08/0.21 % Positive orientable unit clauses : 2
% 0.08/0.21 % Positive unorientable unit clauses: 0
% 0.08/0.21 % Negative unit clauses : 0
% 0.08/0.21 % Non-unit-clauses : 0
% 0.08/0.21 % Current number of unprocessed clauses: 53
% 0.08/0.21 % ...number of literals in the above : 79
% 0.08/0.21 % Current number of archived formulas : 0
% 0.08/0.21 % Current number of archived clauses : 1
% 0.08/0.21 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.21 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.21 % Non-unit clause-clause subsumptions : 0
% 0.08/0.21 % Unit Clause-clause subsumption calls : 0
% 0.08/0.21 % Rewrite failures with RHS unbound : 0
% 0.08/0.21 % BW rewrite match attempts : 1
% 0.08/0.21 % BW rewrite match successes : 1
% 0.08/0.21 % Condensation attempts : 0
% 0.08/0.21 % Condensation successes : 0
% 0.08/0.21 % Termbank termtop insertions : 9574
% 0.08/0.21 % Search garbage collected termcells : 4536
% 0.08/0.21
% 0.08/0.21 % -------------------------------------------------
% 0.08/0.21 % User time : 0.002 s
% 0.08/0.21 % System time : 0.007 s
% 0.08/0.21 % Total time : 0.009 s
% 0.08/0.21 % Maximum resident set size: 5036 pages
% 0.08/0.21
% 0.08/0.21 % -------------------------------------------------
% 0.08/0.21 % User time : 0.011 s
% 0.08/0.21 % System time : 0.014 s
% 0.08/0.21 % Total time : 0.025 s
% 0.08/0.21 % Maximum resident set size: 5632 pages
% 0.08/0.21 % E exiting
%------------------------------------------------------------------------------